Web: http://www.ima.umn.edu | Email: ima-staff@ima.umn.edu | Telephone: (612) 624-6066 | Fax: (612) 626-7370
Additional newsletters available at http://www.ima.umn.edu/newsletters

IMA Newsletter #363

January 2007

2006-2007 Program

Applications of Algebraic Geometry

See http://www.ima.umn.edu/2006-2007 for a full description of the 2006-2007 program on Applications of Algebraic Geometry.

Opportunities at the IMA - There is still time to apply: If you are interested or know of anyone who is interested in applying for one of the IMA General Membership, New Directions Professorship or Postdoctoral Fellowship positions in connection with the 2007-2008 thematic program: Mathematics of Molecular and Cellular Biology, the deadline for applying for these positions is January 5, 2007. You can find the applications for these positions at our Applications site.

New Directions Short Course: The IMA is currently accepting applications for the 2007 New Directions Short Course - Compressive Sampling and Frontiers in Signal Processing June 4 - 15, 2007, taught by Emmanuel Candes, Ron DeVore and Rich Barniuk. This exploding area of research has connections to many areas of mathematics and presents many research opportunities. No prior background in signal processing is expected. Participants will receive full travel and lodging support during the workshop. Participation is by application only. Application deadline: April 1, 2007.

IMA is seeking a new director: The IMA is looking for a new director to begin in summer 2008.

IMA Events

IMA Tutorial

Algebraic Algorithms in Optimization

January 12-13, 2007

Organizers: Niels Lauritzen (Aarhus University), Rekha R. Thomas (University of Washington)

IMA Annual Program Year Workshop

Optimization and Control

January 16-20, 2007

Organizers: Dimitris Bertsimas (Massachusetts Institute of Technology), J. William Helton (University of California, San Diego), Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS)), Mihai Putinar (University of California)

Public Lecture

Dr. Christopher J. Budd

January 18, 2007

Schedule

Monday, January 1

All DayNew Year's Day. The IMA is closed.

Wednesday, January 10

11:15a-12:15pAlgebraic geometry and applications seminar: Algorithms in algebraic analysisAnton Leykin (University of Minnesota Twin Cities)Lind Hall 409 AGS

Friday, January 12

8:00a-8:30aCoffee and RegistrationEE/CS 3-176 T1.12-13.07
8:30a-8:40aWelcome and opening remarksDouglas N. Arnold (University of Minnesota Twin Cities)EE/CS 3-180 T1.12-13.07
8:40a-9:30aGröebner basis methods in integer programming (Lecture Part I) Edwin O'Shea (University of Kentucky)EE/CS 3-180 T1.12-13.07
9:30a-10:00aCoffeeEE/CS 3-176 T1.12-13.07
10:00a-10:50aHands on exercises assisted by Tristram Bogart (Tutorial Part I)Edwin O'Shea (University of Kentucky)Lind Hall 400 T1.12-13.07
11:00a-11:50aGröebner basis methods in integer programming (Lecture Part II)Edwin O'Shea (University of Kentucky)EE/CS 3-180 T1.12-13.07
11:50a-1:30pLunch T1.12-13.07
1:30p-2:20pHands on exercises assisted by Tristram Bogart (Tutorial Part II)Edwin O'Shea (University of Kentucky)Lind Hall 400 T1.12-13.07
2:20p-2:40pCoffeeEE/CS 3-176 T1.12-13.07
2:40p-3:30pOptimization over polynomials with moment matrices and sums of squares

Remarks: (Due to visa problems Monique Laurent was not be able to attend the tutorial. Jean Bernard Lasserre substituted for Monique Laurent.)

Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS))EE/CS 3-180 T1.12-13.07
3:30p-3:50pCoffeeEE/CS 3-176 T1.12-13.07
3:50p-4:40pOptimization over polynomials with moment matrices and sums of squares(continued)Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS))EE/CS 3-180 T1.12-13.07

Saturday, January 13

8:30a-9:00aCoffeeEE/CS 3-176 T1.12-13.07
9:00a-9:50aOptimization over polynomials with moment matrices and sums of squares(continued)Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS))EE/CS 3-180 T1.12-13.07
9:50a-10:20aCoffeeEE/CS 3-176 T1.12-13.07
10:20a-11:10aDemonstration of softwareHartwig Bosse (Center for Mathematics and Computer Science (CWI))EE/CS 3-180 T1.12-13.07
11:20a-12:10p Generating functions for integer optimization (part I)Jesus Antonio De Loera (University of California)EE/CS 3-180 T1.12-13.07
12:10p-1:30pLunch T1.12-13.07
1:30p-2:20p Generating functions for integer optimization (part I)-continuedJesus Antonio De Loera (University of California)EE/CS 3-180 T1.12-13.07
2:20p-2:50pCoffeeEE/CS 3-176 T1.12-13.07
3:00p-3:50pGenerating functions for integer optimization (part II)Jesus Antonio De Loera (University of California)EE/CS 3-180 T1.12-13.07
4:00p-5:00pDemo and introduction to LattEJesus Antonio De Loera (University of California)EE/CS 3-180 T1.12-13.07

Monday, January 15

All DayMartin Luther King, Jr. holiday (IMA is closed)

Tuesday, January 16

8:30a-9:15aCoffee and RegistrationEE/CS 3-176 W1.16-20.07
9:15a-9:30aWelcome and IntroductionDouglas N. Arnold (University of Minnesota Twin Cities) W1.16-20.07
9:30a-10:20aComplexity of multivariate optimization using exact arithmetic Marie-Francoise Roy (Université de Rennes I)EE/CS 3-180 W1.16-20.07
10:20a-11:00aCoffeeEE/CS 3-176 W1.16-20.07
11:00a-11:50aOn the Lovasz theta-number of almost regular graphs with application to Erdos-Renyi graphsEtienne de Klerk (Katholieke Universiteit Brabant (Tilburg University))EE/CS 3-180 W1.16-20.07
11:50a-2:00pLunch W1.16-20.07
2:00p-2:50pOptimization of polynomials on the unit sphereAlexander Barvinok (University of Michigan)EE/CS 3-180 W1.16-20.07
3:00p-3:30pSecond ChancesEE/CS 3-180 W1.16-20.07
3:40p-4:00pGroup photos W1.16-20.07
4:00p-6:30pIMA Reception and Poster SessionLind Hall 400 W1.16-20.07
Recent progress in applying semidefinite optimization to the satisfiability problemMiguel F. Anjos (University of Waterloo)
Solving polynomial systems via LMIsGraziano Chesi (University of Hong Kong)
Computing the best low rank approximation of a matrixKenneth R. Driessel (Iowa State University)
Obstacle-sensitive gain scheduling using semidefinite programmingEric Feron (Georgia Institute of Technology)
Application of semidefinite programming to eigenvalue problems for elliptic linear partial differential equationsCarlos R. Handy (Texas Southern University)
Experiments with linear and semidefinite relaxations for solving the minimum graph bisection problemChristoph Helmberg (Technische Universität Chemnitz-Zwickau)
Advances on the BMV trace conjectureChristopher Hillar (Texas A & M University)
Graphs of transportation polytopesEdward D. Kim (University of California)
SparsePOP and numerical resultsSunyoung Kim (Ewha Womans University)
Inverse dynamical analysis of gene networks using sparsity-promoting regularization James Lu (Johann Radon Institute for Computational and Applied Mathematics )
An exact characterization of bad semidefinite programsGabor Pataki (University of North Carolina)
Distributed optimization in an energy-constrained networkSeid Alireza Razavi Majomard (University of Minnesota Twin Cities)
Semidefinite characterization and computation of real radical idealsPhilipp Rostalski (Eidgenössische TH Zürich-Hönggerberg)
A PARALLEL conic interior point decomposition approach for BLOCK ANGULAR semidefinite programsKartik K. Sivaramakrishnan (North Carolina State University)
Stability region analysis using simulations and sum-of-squares programmingUfuk Topcu (University of California)
Sensor network localization, Euclidean distance matrix completions, and graph realizationHenry Wolkowicz (University of Waterloo)
SeDuMi: a package for conic optimizationYuriy Zinchenko (McMaster University)
Numerical optimization assisted by noncommutative symbolic algebraMauricio de Oliveira (University of California, San Diego)

Wednesday, January 17

9:00a-9:30aCoffeeEE/CS 3-176 W1.16-20.07
9:30a-10:20aComplexity aspects of SDP relaxations of polynomial optimization problemsMarkus Schweighofer (Universität Konstanz)EE/CS 3-180 W1.16-20.07
10:20a-11:00aCoffeeEE/CS 3-176 W1.16-20.07
11:00a-11:50aCoprime factorizations and reduction of linear parameter-varying systems Carolyn Beck (University of Illinois at Urbana-Champaign)EE/CS 3-180 W1.16-20.07
11:50a-1:40pLunch W1.16-20.07
1:40p-2:30pConservative structured noncommutative multidimensional linear systems: realization theory and bounded real lemmaJoseph A. Ball (Virginia Polytechnic Institute and State University)EE/CS 3-180 W1.16-20.07
2:30p-3:00pCoffeeEE/CS 3-176 W1.16-20.07
3:00p-3:50pMatrix convexity, matrix inequalities, and beyondScott McCullough (University of Florida)EE/CS 3-180 W1.16-20.07
4:00p-4:30pSecond ChancesEE/CS 3-180 W1.16-20.07
6:30p-8:30pGroup DinnerKikugawa at Riverplace (Japanese Restaurant)
43 Main Street SE Minneapolis MN 55414 612-378-3006
W1.16-20.07

Thursday, January 18

9:00a-9:30aCoffeeEE/CS 3-176 W1.16-20.07
9:30a-10:30aThe algebraic degree of semidefinite programmingBernd Sturmfels (University of California)EE/CS 3-180 W1.16-20.07
10:20a-11:00aCoffeeEE/CS 3-176 W1.16-20.07
11:00a-11:50aSharp thresholds for sparsity recovery in the high-dimensional and noisy setting using l_1 relaxations Martin J. Wainwright (University of California)EE/CS 3-180 W1.16-20.07
11:50a-1:40pLunch W1.16-20.07
1:40p-2:30pSums of squares, gradient ideals, and optimizationVictoria Powers (Emory University)EE/CS 3-180 W1.16-20.07
2:30p-3:00pCoffeeEE/CS 3-176 W1.16-20.07
3:00p-3:50pPolynomial optimal control with GloptiPoly 3.0 Didier Henrion (Centre National de la Recherche Scientifique (CNRS))EE/CS 3-180 W1.16-20.07
4:00p-4:30pSecond ChancesEE/CS 3-180 W1.16-20.07
5:00p-6:30pReceptionLind Hall 400 W1.16-20.07
7:00p-8:00pMath matters - IMA public lecture: Making sense of a complex worldChristopher J. Budd (University of Bath)Willey Hall 125 PUB1.18.07
7:00p-8:00pMath matters - IMA public lecture: Making sense of a complex worldChristopher J. Budd (University of Bath)Willey Hall 125 W1.16-20.07

Friday, January 19

9:00a-9:30aCoffeeEE/CS 3-176 W1.16-20.07
9:30a-10:20aEstimation of sparse graphical modelsLaurent El Ghaoui (University of California)EE/CS 3-180 W1.16-20.07
10:20a-11:00aCoffeeEE/CS 3-176 W1.16-20.07
11:00a-11:50aDiscrete optimization under moment uncertainty: complexity, persistency and asymptoticsDimitris Bertsimas (Massachusetts Institute of Technology)EE/CS 3-180 W1.16-20.07
11:50a-2:30pLunch W1.16-20.07
2:30p-3:20pLMI representation of convex setsVictor Vinnikov (Ben Gurion University of the Negev)EE/CS 3-180 W1.16-20.07
3:30p-4:00pSecond Chances EE/CS 3-180 W1.16-20.07

Saturday, January 20

9:00a-9:30aCoffeeEE/CS 3-176 W1.16-20.07
9:30a-10:20aSparsity in polynomial optimizationMasakazu Kojima (Tokyo Institute of Technology)EE/CS 3-180 W1.16-20.07
10:20a-11:00aCoffeeEE/CS 3-176 W1.16-20.07
11:00a-11:50aApproximation of positive polynomials by sums of squaresSalma Kuhlmann (University of Saskatchewan)EE/CS 3-180 W1.16-20.07
11:50a-2:30pLunch W1.16-20.07
2:30p-3:20pConvex sets with lifted semidefinite representationJean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS))EE/CS 3-180 W1.16-20.07
3:30p-4:00p Second Chances and closing remarksEE/CS 3-180 W1.16-20.07

Tuesday, January 23

11:15a-12:15pIMA postdoc seminar: On the quality bound of low order SOS relaxationsJiawang Nie (University of Minnesota Twin Cities)Lind Hall 409 PS

Wednesday, January 24

11:15a-12:15pAlgebraic geometry and applications seminar: Moments of positivityMihai Putinar (University of California)Lind Hall 409 AGS

Thursday, January 25

11:15a-12:15pReal algebraic geometry tutorial: Semi-algebraic sets and functionsKenneth R. Driessel (Iowa State University)Lind Hall 409 RAG

Friday, January 26

Tuesday, January 30

11:15a-12:15pIMA postdoc seminar: Syzygies of toric varietiesMilena Hering (University of Minnesota Twin Cities)Lind Hall 409 PS

Wednesday, January 31

11:15a-12:05pAlgebraic geometry and applications seminar: "SDP and LP-relaxations in polynomial optimization: The power of real algebraic geometry" Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS))Lind Hall 229 AGS
Abstracts
Second Chances
Abstract: No Abstract
Miguel F. Anjos (University of Waterloo) Recent progress in applying semidefinite optimization to the satisfiability problem
Abstract: Extending the work of de Klerk, Warners and van Maaren, we propose new semidefinite programming (SDP) relaxations for the satisfiability (SAT) problem. The SDP relaxations are partial liftings motivated by the Lasserre hierarchy of SDP relaxations for 0-1 optimization problems. Theoretical and computational results show that these relaxations have a number of favourable properties, particularly as a means to prove that a given SAT formula is unsatisfiable, and that this approach compares favourably with existing techniques for SAT.
Joseph A. Ball (Virginia Polytechnic Institute and State University) Conservative structured noncommutative multidimensional linear systems: realization theory and bounded real lemma
Abstract: By a noncommutative multidimensional linear system we mean a linear discrete-time input/state/output system with evolution along a finitely generated free semigroup. A formal Z-transform of the input-output map results in a transfer function equal to a formal power series in noncommuting indeterminates with operator (or matrix) coefficients. If one imposes energy-balance inequalities and additional structure to the system equations, the resulting transfer function is a formal power series with the additional structure of interest for analyzing the robust control problem for a plant with linear-fractional-modeled time-varying structured uncertainty. The Bounded Real Lemma for such systems is closely connected with work of Paganini on the robust control of such systems. An abelianization of the system equations leads to systems with evolution along a multidimensional integer lattice with transfer function equal to a linear-fractional expression in several commuting variables of Givon-Roesser, Fornasini-Marchesini or other structured types. Connections with the automata theory of Schuetzenberger, Fliess, Eilenberg and others from the 1960s will also be discussed. This talk reports on joint work of the speaker with Tanit Malakorn (Naresuan University, Thailand) and Gilbert Groenewald (North West University, South Africa).
Alexander Barvinok (University of Michigan) Optimization of polynomials on the unit sphere
Abstract: We consider the problem of computing the maximum absolute value of a real multivariate polynomial on the unit sphere. We identify a class of polynomials for which the problem admits a randomized polynomial time approximation algorithm consisting in computing the maximum absolute value of the restriction of the polynomial onto a random subspace of logarithmic dimension and scaling the result. The characteristic feature of polynomials admitting such an algorithm is that they are "focused": the ratio of their maximum absolute value and the L2 norm is large.
Carolyn Beck (University of Illinois at Urbana-Champaign) Coprime factorizations and reduction of linear parameter-varying systems
Abstract: We present a complete derivation of coprime factorizations for a class of multi-dimensional systems containing linear parameter-varying and uncertain systems. A generalization of coprime factors model reduction using a balanced truncation approach is then given, with error bounds on the factorized mapping in the l2-induced norm. The proposed reduction method is thus applicable to linear parameter-varying and uncertain systems that do not satisfy the usual l2-induced stability constraint required by the standard non-factored truncation methods.
Dimitris Bertsimas (Massachusetts Institute of Technology) Discrete optimization under moment uncertainty: complexity, persistency and asymptotics
Abstract: We address the problem of evaluating the expected optimal objective value of a discrete optimization problem under uncertainty in the objective coefficients. The probabilistic model we consider prescribes limited marginal distributional information for the objective coefficients in the form of moments. We show that for a fairly general class of marginal information, a tight upper (lower) bound on the expected optimal objective value of a discrete maximization (minimization) problem can be computed in polynomial time if the corresponding deterministic discrete optimization problem is solvable in polynomial time. We provide an efficiently solvable semidefinite programming formulation to compute this tight bound. We use the insights from this analysis to: a) understand the percistency of a decision variable, i.e., the probability that it is part of an optimal solution; for instance, in project scheduling, when the task activity times are random, the challenge is to determine a set of critical activities that will potentially lie on the longest path; b) to analyze the asymptotic behavior of a general class of combinatorial problems that includes the linear assignment, spanning tree and traveling salesman problems, under knowledge of complete marginal distributions, with and without independence. We calculate the limiting constants exactly. (joint work with Karthik Natarajan and Chung Piaw Teo)
Hartwig Bosse (Center for Mathematics and Computer Science (CWI)) Demonstration of software
Abstract: No Abstract
Christopher J. Budd (University of Bath) Math matters - IMA public lecture: Making sense of a complex world
Abstract: The world around us often seems terribly complex, chaotic and difficult to understand. We encounter this every day: in the weather, social networks, sophisticated machinery, the internet. Frequently this complexity arises from the interaction of widely diverse scales in time and space. For example, the weather can turn in minutes, while the climate persists for many many years. Can math and science help us to make sense of all this complexity, or is it a study doomed from the start? Illustrating with many examples, Professor Budd will show that all is not lost. He will explain how simple properties often emerge from seemingly very complex systems, and how we can use these properties to gain understanding.
Graziano Chesi (University of Hong Kong) Solving polynomial systems via LMIs
Abstract: Joint work with Y.S. Hung. The problem of computing the solution of systems of polynomial equalities and inequalities is considered. First, it is shown that the solutions of these systems can be found by looking for vectors with polynomial structure in linear spaces obtained via a convex LMI optimization. Then, it is shown that an upper bound to the dimension of the linear spaces where the sought solutions are looked for can be imposed in a non-conservative way by imposing suitable linear matricial constraints. This allows one to obtain the linear spaces with the smallest dimension, which is important because the solutions can be extracted only if the dimension of the linear spaces is smaller than a certain threshold. Moreover, the proposed approach allows one to improve the numerical accuracy of the extraction mechanism.
Jesus Antonio De Loera (University of California) Demo and introduction to LattE
Abstract: No Abstract
Kenneth R. Driessel (Iowa State University) Computing the best low rank approximation of a matrix
Abstract: Consider the following Problem: Given an m-by-n real matrix A and a positive integer k, find the m-by-n matrix with rank k that is closest to A. (I use the Frobenius inner product.) I shall present a rank-preserving differential equation (d.e.) in the space of m-by-n real matrices which solves this problem. In particular, I shall show that if X(t) is a solution of this d.e. then the distance between X(t) and A decreases; in other words, this distance function is a Lyapunov function for the d.e. I shall also show that (generically) this d.e. converges to a unique stable equilibrium point. This point is the solution of the given problem.
Laurent El Ghaoui (University of California) Estimation of sparse graphical models
Abstract: The graphical model formalism allows to describe multivariate probability distributions using a graph where random variables are represented by nodes, and the absence of an edge corresponds to conditional independence. While this formalism is very general, the corresponding maximum-likelihood problem is often challenging numerically. In addition, one often needs to obtain a graph that is sparse, in order to enhance interpretability of the result. In this talk, we examine the problem where log-likelihood function is penalized by an l-one norm term to encourage sparsity, in two special cases,first for Gaussian then for Boolean variables. In the Gaussian case, we discuss first-order methods and a block- coordinate descent algorithm. For Boolean random variables, the problem is NP-hard, due to an exponential number of terms in the log-likelihood function. We discuss two approximations, one based on Wainwright and Jordan's log- determinant approximation (2005), and another based on lifting and rank relaxation.
Eric Feron (Georgia Institute of Technology) Obstacle-sensitive gain scheduling using semidefinite programming
Abstract: Joint work with Mazen Farhood. We present an application of semidefinite programming techniques to the regulation of vehicle trajectories in the vicinity of obstacles. We design control laws, together with Lyapunov functions that guarantee closed-loop stability and performance of the vehicle's regulation loop. These control laws are easy to implement and automatically "relax the system's gains" when away from the obstacles, while tightening them when obstacle proximity is detected.
Carlos R. Handy (Texas Southern University) Application of semidefinite programming to eigenvalue problems for elliptic linear partial differential equations
Abstract: The calculation of eigenvalues for stiff elliptic linear partial differential equations (LPDEs) can be plagued with significant inaccuracies depending on the "estimation" methods used (i.e. variational, finite differencing, asymptotic analysis, perturbative, Galerkin, etc.). A preferred approach is to be able to generate tight, converging lower and upper bounds to the eigenvalues, thereby removing any uncertainties in the reliability of the generated results. Twenty years ago one such method was developed by Handy, Bessis, and co-workers [1-3]. This general approach is referred to as the Eigenvalue Moment Method (EMM) and involves a Semidefinite Programming formalism coupled with a Linear Programming based “Cutting Algorithm.” It makes use of well known nonnegativity properties of Sturm-Liouville type systems combined with important theorems from the classic Moment Problem. The EMM procedure has been used to solve a variety of LPDEs on various support spaces (i.e. unbounded, semi-bounded, bounded, periodic, discrete). Equivalent gradient search variational reformulations, exploiting higher levels of convexity, have also been developed leading to the Volcano Function representation [4]. It is also possible to extend EMM to certain non-hermitian systems of importance in forefront areas in mathematical physics. Here too, the EMM approach can yield converging lower and upper bounds to the real and imaginary parts of the complex eigenvalues (or other physical parameters) [5]. More recently EMM was broadened (exploiting certain quasi-convexity properties and the generalized eigenvlaue problem) in order to convexify a multi-extrema plagued procedure in mathematical physics [6]. We outline the important EMM results achieved over the last two decades. 1. C. R. Handy and D. Bessis, "Rapidly Convergent Lower Bounds for the Schrodinger Equation Ground State Energy," Phys. Rev. Lett. 55, 931 (1985).
2. C. R. Handy, D. Bessis, and T. R. Morley, "Generating Quantum Energy Bounds by the Moment Method: A Linear Programming Approach," Phys. Rev. A 37, 4557 (1988).
3. C. R. Handy, D. Bessis, G. Sigismondi, and T. D. Morley, "Rapidly Converging Bounds for the Ground State Energy of Hydrogenic Atoms in Superstrong Magnetic Fields," Phys. Rev. Lett. 60, 253 (1988).
4. C. R. Handy, K. Appiah, and D. Bessis "Moment-Problem Formulation of a Minimax Quantization Procedure", Phys. Rev. A 50, 988 (1994).
5. C. R. Handy, "Generating Converging Bounds to the (Complex) Discrete States of the P2 + iX3 + iaX Hamiltonian," J. Phys. A: Math. Gen. 34, 5065 (2001).
6. C. R. Handy “(Quasi)-convexification of Barta’s (multi-extrema) bounding theorem," J. Phys. A: Math. Gen. 39, 3425 (2006)
Christoph Helmberg (Technische Universität Chemnitz-Zwickau) Experiments with linear and semidefinite relaxations for solving the minimum graph bisection problem
Abstract: Given a graph with node weights, the convex hull of the incidence vectors of all cuts satisfying a weight restricition on each side is called the bisection cut polytope. We study the facial structure of this polytope which shows up in many graph partitioning problems with applications in VLSI-design or frequency assignment. We give necessary and in some cases sufficient conditions for the knapsack tree inequalities introduced in Ferreira et al. 1996 to be facet-defining. We extend these inequalities to a richer class by exploiting that each cut intersects each cycle in an even number of edges. Furthermore, we present a new class of inequalities that are based on non-connected substructures yielding non-linear right-hand sides. We show that the supporting hyperplanes of the convex envelope of this non-linear function correspond to the faces of the so-called cluster weight polytope, for which we give a complete description under certain conditions. Finally, we incorporate cutting planes algorithms based on the presened inequalities in a branch-and-cut framework and discuss their interaction with the linear and semidefinite relaxation.
Didier Henrion (Centre National de la Recherche Scientifique (CNRS)) Polynomial optimal control with GloptiPoly 3.0
Abstract: Joint work by Jean-Bernard Lasserre, Johan Löfberg, Christophe Prieur and Emmanuel Trélat. The new release 3.0 of the Matlab package GloptiPoly is introduced through an application to a class of nonlinear optimal control problems for which the data (differential equations, state and control constraints, cost) are multivariate polynomials. GloptiPoly 3.0 is aimed at solving generalized moment problems. It allows to manipulate several measures and define linear decision problems on their moments. The problems can then be solved numerically with any semidefinite programming solver interfaced with YALMIP.
Milena Hering (University of Minnesota Twin Cities) IMA postdoc seminar: Syzygies of toric varieties
Abstract: Understanding the equations defining algebraic varieties and the relations, or syzygies, between them is a classical problem in algebraic geometry. Green showed that sufficient powers of ample line bundles induce a projectively normal embedding that is cut out by quadratic equations and whose first q syzygies are linear. In this talk I will present numerical criteria for line bundles on toric varieties to satisfy this property. I will also discuss criteria for the coordinate ring of such an embedding to be Koszul.
Christopher Hillar (Texas A & M University) Advances on the BMV trace conjecture
Abstract: We discuss some progress on a long-standing conjecture in mathematical physics due to Bessis, Moussa, and Villani (1975). The statement is enticingly simple (thanks to a reformulation by Elliot Lieb and Robert Seiringer): For every positive integer m and every pair of positive semidefinite matrices A and B, the polynomial

p(t) = Tr[(A+tB)m]

has nonnegative coefficients. Our approach allows for several reductions to this difficult conjecture. For instance, it would be enough to show that a nonzero (matrix) coefficient (A+tB)m has at least 1 positive eigenvalue. Additionally, if the conjecture is true for infinitely many m, then it is true for all m. Finally, two challenges to the SOS community are proposed: Prove the conjecture in dimension 3 for m = 6 (known) and m = 7 (unknown).
Edward D. Kim (University of California) Graphs of transportation polytopes
Abstract: Joint work with Jesus A. de Loera (University of California, Davis). Transportation polytopes are well-known objects in operations reseach and mathematical programming. These polytopes have very quick tests for feasiblity, coordinates of a vertex can be quickly determined, and they have nice embedding properties: every polytope can be viewed as a certain kind of transportation polytope. Using the notion of chamber complex, Gale diagrams, and the theory of secondary polytopes we are able to exhaustively and systematically enumerate all combinatorial types of nondegenerate transportation polytopes of small sizes. These generic polytopes (those of maximal dimension whose vertices are simple) will have the largest graph diameters and vertex counts in their class. Using our exhaustive lists, we give results on some of the conjectures of Yemelichev, Kovalev, and Kratsov. In particular, this poster focuses on questions related to the 1-skeleton graph of these polyhedra. The study of 1-skeleta of these polytopes are fundamental in attempting to consider the complexity of the simplex method of linear programming.
Sunyoung Kim (Ewha Womans University) SparsePOP and numerical results
Abstract: SparesPOP is MATLAB implementation of a sparse semidefinite programming (SDP) relaxation method proposed for polynomial optimization problems (POPs) in the recent paper by Waki, Kim, Kojima and Muramatsu. The sparse SDP relaxation is based on "a hierarchy of LMI relaxations of increasing dimensions" by Lasserre, and exploits a sparsity structure of polynomials in POPs. The efficiency of SparsePOP to compute bounds for optimal values of POPs is increased and larger scale POPs can be handled. Numerical results are shown to illustrate the perfomance of SparsePOP.
Masakazu Kojima (Tokyo Institute of Technology) Sparsity in polynomial optimization
Abstract: A polynomial optimization problem (POP) is a problem of minimizing a polynomial objective function subject to polynomial equalities and inequalities. It is getting popular to apply the sum of squares (SOS) relaxation to compute global minimum solutions of a POP. The SOS relaxation problem is reduced to a semidefinite programming problem (SDP), which we can solve by applying the primal-dual interior-point method. In this process, exploiting sparsity is essential in solving a large-scale POP. We present "correlative sparsity," a certain structured sparsity of a POP which is characterized as a sparse Cholesky factorization of an aggregated sparsity pattern matrix of the POP. With this correlative sparsity, we can apply the sparse SOS relaxation to a large-scale POP, and we can solve the resulting SDP efficiently by the primal-dual interior-point method. We also discuss some applications.
Salma Kuhlmann (University of Saskatchewan) Approximation of positive polynomials by sums of squares
Abstract: Approximation of positive polynomials by sums of squares has important applications to polynomial optimisation. In this talk, I will survey the main recent results achieved on that topic: I will consider positive (respectively, non-negative) polynomials on compact (respectively, unbounded) semi-algebraic sets. I will discuss representations in the associated preorderings (respectively, linear representations in the associated quadratic module). The representation often depends on the dimension of the semi-algebraic set; I will present stronger results in the low dimensional case. I will also highlight special representations when the positive polynomials under consideration are sparse (that is, satisfy some separation and overlap conditions on the variables appearing in the monomials).
Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS)) Algebraic geometry and applications seminar: "SDP and LP-relaxations in polynomial optimization: The power of real algebraic geometry"
Abstract: Summary: In this seminar we consider the general polynomial optimization problem: that is, finding the GLOBAL minimum of a polynomial over a compact basic semi-algebraic set, a NP-hard problem. We will describe how powerful representation results in real algebraic geometry are exploited to build up a hierarchy of linear or semidefinite programming (LP or SDP) relaxations, whose monotone sequence of optimal values converges to the desired value. A comparison with the usual Kuhn-Tucker local optimality conditions is also discussed.
Anton Leykin (University of Minnesota Twin Cities) Algebraic geometry and applications seminar: Algorithms in algebraic analysis
Abstract: In the first part of this talk I will give an introduction to the algorithmic theory of D-modules. This would include the description of the properties of the rings of differential operators, in particular, the ones that allow for computation of Gröbner bases. The second part will show the applications of D-modules to the computation of local cohomology of a polynomial ring at a given ideal. The nonvanishing of the local cohomology module of a certain degree may answer the question about the minimal number of generators for the ideal. The presentation is going to be accompanied by the demonstration of the relevant computations in the D-modules for Macaulay 2 package.
James Lu (Johann Radon Institute for Computational and Applied Mathematics ) Inverse dynamical analysis of gene networks using sparsity-promoting regularization
Abstract: Given an ODE model for a biological system, the forward problem consists of determining its solution behavior. However, many biological questions are of the inverse type: what are the possible dynamics that can arise out of the model? how is the control mechanism encoded in the topology of the regulatory network? We propose inverse dynamical analysis as a methodology for addressing various questions that arise in studying biological systems, from the initial modelling to the proposal of new experiments. In addition, once a satisfactory model has been developed, the method can be used to design various bifurcation phenotypes that exhibit certain dynamical properties. To summarize, the proposed methodology consists of the following two inverse analyses:
  • inverse eigenvalue analysis, to probe and characterize parameter combinations leading to changes in the qualitative dynamics;
  • inverse bifurcation analysis, to identify and design mechanisms that can give rise to a set of bifurcation phenotypes.
In our work, we use sparsity-promoting regularization functional to 'sparsely' map dynamical behaviors to parameter sets. In combination with hierarchical identification strategies, the underlying mechanisms can be elucidated. We demonstrate some applications, from exploring possible evolutionary scenarios to analyzing influential interactions in a cell phase transition model.
Arash Mafi (Corning) IMA/MCIM Industrial problems seminar: A compact high power singlemode microstructured fiber laser
Abstract: We will discuss the design and fabrication of a compact, high power, singlemode, microstructured (photonic crystal) fiber laser. A low index core (antiguiding) assisted by the geometry of the microstructure is used to maximize the core size while maintaining the number of propagating modes. Beam quality factor (M2) is studied for these fibers and is successfully used as a design tool. Some design concepts for scaling up the power using single-supermode multicore microstructure fibers will also be discussed.
Scott McCullough (University of Florida) Matrix convexity, matrix inequalities, and beyond
Abstract: Many ideas from convex analysis and real algebraic geometry extend canonically to the operator space setting giving rise to the notions of matrix (non-commutative) convex sets and functions. These notions also model matrix inequalities which are scalable in the sense that they do not explicitly depend upon the size of the matrices involved. This talk will survey matrix convexity emphasizing the rigid nature of convexity in the non-commutative semi-algebraic setting. It may aslo include a discussion of characterizing factorizations of a non-commutative polynomial in terms of the signature of its Hessian.
Edwin O'Shea (University of Kentucky) Hands on exercises assisted by Tristram Bogart (Tutorial Part II)
Abstract: No Abstract
Gabor Pataki (University of North Carolina) An exact characterization of bad semidefinite programs
Abstract: SDP's duality theory has been somewhat less well studied than its algorithmic aspects. Strong duality, — expected in linear programming fails in many cases, and the variety of how things can go wrong is bewildering: one can have nonattainment in either one of the primal and the dual problems, attainment on both sides, but a finite duality gap, etc. The main result we present in this talk is a surprisingly simple, exact, "excluded minor" type characterization of all semidefinite systems that have a badly behaved dual for some objective function. The characterization is based on some new, fundamental results in convex analysis on the closedness of the linear image of a closed convex cone. In particular, our result is a necessary condition for the closedness of the linear image — as opposed to the usual sufficient conditions, such as the existence of a Slater-point, or polyhedrality. Our conditions are necessary and sufficient, when the cone belongs to a large class, called nice cones.
Victoria Powers (Emory University) Sums of squares, gradient ideals, and optimization
Abstract: We discuss algorithms for optimizing polynomials on semialgebraic sets using representation theorems from real algebraic geometry for positive polynomials. In the case of compact semialgebraic sets, the method of Lasserre generates a sequence of SDP relaxations which converge to the solution, however this method does not always work in the non-compact case. We will discuss work of Demmel, Nie, and Sturmfels in the global case and joint work with Demmel and Nie in the case of non-compact semialgebraic sets.
Mihai Putinar (University of California) Algebraic geometry and applications seminar: Moments of positivity
Abstract: The seminar will offer an unifying overview of the theory of positive functionals, the spectral theorem, moment problems and polynomial optimization. We will treat only the commutative case, in the following order: 1. The integral 2. Positive definite quadratic forms and the spectral theorem 3. Orhtogonal polynomials and Jacobi matrices 4. Moment problems and continued fractions 5. Polynomial optimization 6. Open questions We encourage the participants to have a look at Stieltjes' classical memoir on continued fractions, available at: http://www.numdam.org/numdam-bin/fitem?id=AFST_1894_1_8_4_J1_0
Seid Alireza Razavi Majomard (University of Minnesota Twin Cities) Distributed optimization in an energy-constrained network
Abstract: We consider a distributed optimization problem whereby two nodes S1 and S2 wish to jointly minimize a common convex quadratic cost function f(x1; x2), subject to separate local constraints on x1 and x2, respectively. Suppose that node S1 has control of variable x1 only and node S2 has control of variable x2 only. The two nodes locally update their respective variables and periodically exchange their values over a noisy channel. Previous studies of this problem have mainly focused on the convergence issue and the analysis of convergence rate. In this work, we focus on the communication energy and study its impact on convergence. In particular, we consider a class of distributed stochastic gradient type algorithms implemented using certain linear analog messaging schemes. We study the minimum amount of communication energy required for the two nodes to compute an epsilon-minimizer of f(x1; x2) in the mean square sense. Our analysis shows that the communication energy must grow at least at the rate of (1/epsilon). We also derive specific designs, which attain this minimum energy bound, and provide simulation results that confirm our theoretical analysis. Extension to the multiple node case is described.
Philipp Rostalski (Eidgenössische TH Zürich-Hönggerberg) Semidefinite characterization and computation of real radical ideals
Abstract: Joint work with J.-B. Lasserre and M. Laurent. For an ideal given by a set of generators, h_1...h_m \in R[x] a new semidefinite characterization of its real radical ideal I(V_R(I))is presented, provided it is zero-dimensional (even if I is not). Moreover we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety V_R=V(I) \subset R^n as well as generators of the real radical ideal. The latter are obtained in the form of border or Gröbner bases. The algorithm is based on moment relaxations and, in contrast to other existing methods, it exploits the real algebraic nature of the problem right from the beginning and avoids the computation of complex components.
Marie-Francoise Roy (Université de Rennes I) Complexity of multivariate optimization using exact arithmetic
Abstract: Global optimization of polynomial functions under polynomial constraints will be related to general algorithmic problems in real algebraic geometry and the current existing complexity results discussed. The results in the special case of quadratic polynomials will be described. Main reference for the talk: S. Basu, R. Pollack, M.-F. Roy: Algorithms in real algebraic geometry, Springer, second edition (2006)
Markus Schweighofer (Universität Konstanz) Complexity aspects of SDP relaxations of polynomial optimization problems
Abstract: We discuss complexity aspects of Lasserre's sequence of SDP relaxations of a given polynomial optimization problem. As a special example where a lot is known, we consider the MAXCUT problem. The following topics should be covered:
- the moment problem and convergence to unique minimizers,
- speed of convergence to the optimal value,
- Scheiderers result on stability and the moment problem,
- the approximability result of Goemans and Williamson for MAXCUT, and
- the inapproximability result of Khot, Kindler, Mossel and O'Donnell for MAXCUT.
Kartik K. Sivaramakrishnan (North Carolina State University) A PARALLEL conic interior point decomposition approach for BLOCK ANGULAR semidefinite programs
Abstract: Semidefinite programs (SDPs) with a BLOCK-ANGULAR structure occur routinely in practice. In some cases, it is also possible to exploit the SPARSITY and SYMMETRY in an unstructured SDP, and preprocess it into an equivalent SDP with a block-angular structure. We present a PARALLEL CONIC INTERIOR POINT DECOMPOSITION approach to solve block-angular SDPs. Our aim is to solve such a SDP in an iterative fashion between a master problem (a quadratic conic program); and decomposed and distributed subproblems (smaller SDPs) in a parallel computing environment. We present our computational results with the algorithm on several test instances; our computations were performed on the distributed HENRY2 cluster at North Carolina State University.
Bernd Sturmfels (University of California) The algebraic degree of semidefinite programming
Abstract: Given a semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree counts the critical points attained by a linear functional on a fixed rank locus in a linear space of symmetric matrices. We determine this degree using methods from complex algebraic geometry, such as projective duality, determinantal varieties, and their Chern classes. This is a joint paper with Jiawang Nie and Kristian Ranestad, posted at rxiv.org/abs/math.OC/0611562.
Ufuk Topcu (University of California) Stability region analysis using simulations and sum-of-squares programming
Abstract: The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant subsets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite dimensional polynomial parameterizations for Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of Lyapunov function candidates are assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on several small examples from the literature and a controlled aircraft dynamics problem.
Victor Vinnikov (Ben Gurion University of the Negev) LMI representation of convex sets
Abstract: I will discuss the characterization of convex sets in m which can be represented by Linear Matrix Inequalities, i.e., as feasible sets of semidefinite programmes. There is a simple necessary condition, called rigid convexity, which has been shown to be sufficient for sets in the plane and is conjectured to be sufficient (in a somewhat weakened sense) for any m. This should be contrasted with the situation for matrix convex sets that will feature in the talk of Scott McCullough, where all the available evidence suggests that any matrix convex set with noncommutative algebraic boundary admits an LMI representation. This is a joint work with Bill Helton.
Martin J. Wainwright (University of California) Sharp thresholds for sparsity recovery in the high-dimensional and noisy setting using l_1 relaxations
Abstract: The problem of recovering the sparsity pattern of an unknown signal arises in various domains, including graphical model selection, signal denoising, constructive approximation, compressive sensing, and subset selection in regression. The standard optimization-theoretic formulation of sparsity recovery involves l_0-constraints, and typically leads to computationally intractable optimization problems. This difficulty motivates the development and analysis of approximate methods; in particular, a great deal of work over the past decade has focused on the use of convex l_1-relaxations for sparsity recovery. In this work, we analyze the performance of l_1-constrained quadratic programming for recovering an unknown signal in p dimensions with at most s non-zero entries based on a set of n noisy observations. Of interest is the number of observations n that are required, as a function of the model dimension p and sparsity index s, for exact sparsity recovery. We analyze this question in the high-dimensional setting, in which both the model dimension p and number of observations n tend to infinity. Our main result is to establish, for a broad class of Gaussian measurement ensembles, precise threshold results on the required growth rate for successful recovery using the computationally tractable l_1 relaxation.
Henry Wolkowicz (University of Waterloo) Sensor network localization, Euclidean distance matrix completions, and graph realization
Abstract: We study Semidefinite Programming, SDP, relaxations for Sensor Network Localization, SNL, with anchors and with noisy distance information. The main point of the paper is to view SNL as a (nearest) Euclidean Distance Matrix, EDM, completion problem and to show the advantages for using this latter, well studied model. We first show that the current popular SDP relaxation is equivalent to known relaxations in the literature for EDM completions. The existence of anchors in the problem is not special. The set of anchors simply corresponds to a given fixed clique for the graph of the EDM problem. We next propose a method of projection when a large clique or a dense subgraph is identified in the underlying graph. This projection reduces the size, and improves the stability, of the relaxation. In addition, viewing the problem as an EDM completion problem yields better low rank approximations for the low dimensional realizations. And, the projection/reduction procedure can be repeated for other given cliques of sensors or for sets of sensors, where many distances are known. Thus, further size reduction can be obtained. Optimality/duality conditions and a primal-dual interior-exterior path following algorithm are derived for the SDP relaxations We discuss the relative stability and strength of two formulations and the corresponding algorithms that are used. In particular, we show that the quadratic formulation arising from the SDP relaxation is better conditioned than the linearized form, that is used in the literature and that arises from applying a Schur complement.
Yuriy Zinchenko (McMaster University) SeDuMi: a package for conic optimization
Abstract: No Abstract
Etienne de Klerk (Katholieke Universiteit Brabant (Tilburg University)) On the Lovasz theta-number of almost regular graphs with application to Erdos-Renyi graphs
Abstract: We consider k-regular graphs with loops, and study the Lovasz theta-numbers and Schrijver theta'-numbers of the graphs that result when the loop edges are removed. We show that the theta-number dominates a recent eigenvalue upper bound on the stability number due to Godsil and Newman [C.D. Godsil and M.W. Newman. Eigenvalue bounds for independent sets. Journal of Combinatorial Theory B, to appear]. As an application we compute the theta and theta' numbers of certain instances of Erdos-Renyi graphs. This computation exploits the graph symmetry using the methodology introduced in [E. de Klerk, D.V. Pasechnik and A. Schrijver. Reduction of symmetric semidefinite programs using the regular *-representation. Mathematical Programming B, to appear]. The computed values are strictly better than the Godsil-Newman eigenvalue bounds. (Joint work with Mike Newman, Dima Pasechnik, and Renata Sotirov.)
Mauricio de Oliveira (University of California, San Diego) Numerical optimization assisted by noncommutative symbolic algebra
Abstract: We describe how a symbolic computer algebra tool (NCAlgebra) that can handle symbolic matrix (noncommutative) products is used to numerically solve systems and control problems. Our current focus is on semidefinite programs arising from control theory, where matrix variables appear naturally. Our tools keep matrix variables aggregated at all steps of a primal-dual interior-point algorithm. Symbolic matrix expressions are automatically generated and used on iterative numerical procedures for the determination of search directions, showing promising results.
Visitors in Residence
Cheonghee Ahn Yonsei University 1/4/2007 - 1/23/2007
Suliman Al-Homidan King Fahd University of Petroleum & Minerals 1/16/2007 - 1/20/2007
Elizabeth Allman University of Alaska 1/7/2007 - 4/7/2007
Jungha An University of Minnesota Twin Cities 9/1/2005 - 8/31/2007
Miguel F. Anjos University of Waterloo 1/15/2007 - 1/20/2007
D. Gregory Arnold US Air Force Research Laboratory 1/17/2007 - 1/19/2007
Douglas N. Arnold University of Minnesota Twin Cities 7/15/2001 - 8/31/2007
Donald G. Aronson University of Minnesota Twin Cities 9/1/2002 - 8/31/2007
Michel Baes Katholieke Universiteit Leuven 1/15/2007 - 1/22/2007
Joseph A. Ball Virginia Polytechnic Institute and State University 1/15/2007 - 1/21/2007
Chunsheng Ban Ohio State University 1/15/2007 - 1/20/2007
Alexander Barvinok University of Michigan 1/15/2007 - 1/18/2007
Saugata Basu Georgia Institute of Technology 1/15/2007 - 1/20/2007
Daniel J. Bates University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Carolyn Beck University of Illinois at Urbana-Champaign 1/15/2007 - 1/18/2007
Dimitris Bertsimas Massachusetts Institute of Technology 1/15/2007 - 1/19/2007
Yermal Sujeet Bhat University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Víctor Blanco Izquierdo University of Sevilla 1/11/2007 - 4/21/2007
Cristiano Bocci Università di Milano 1/10/2007 - 3/10/2007
Tristram Bogart University of Washington 1/8/2007 - 3/25/2007
Hartwig Bosse Center for Mathematics and Computer Science (CWI) 1/11/2007 - 1/21/2007
Christopher J. Budd University of Bath 1/16/2007 - 1/21/2007
Constantine M. Caramanis University of Texas 1/15/2007 - 1/20/2007
Enrico Carlini Politecnico di Torino 1/10/2007 - 2/16/2007
Dong Eui Chang University of Waterloo 1/15/2007 - 1/21/2007
Graziano Chesi University of Hong Kong 1/15/2007 - 1/19/2007
Hi Jun Choe Yonsei University 1/5/2007 - 1/20/2007
Ionut Ciocan-Fontanine University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Raul Curto University of Iowa 1/15/2007 - 1/20/2007
Etienne de Klerk Katholieke Universiteit Brabant (Tilburg University) 1/13/2007 - 1/20/2007
Jesus Antonio De Loera University of California 1/11/2007 - 1/20/2007
Mauricio de Oliveira University of California, San Diego 1/15/2007 - 1/19/2007
Xuan Vinh Doan Massachusetts Institute of Technology 1/11/2007 - 1/21/2007
John C. Doyle California Institute of Technology 1/18/2007 - 1/21/2007
Kenneth R. Driessel Iowa State University 9/1/2006 - 6/29/2007
Michael Dritschel University of Newcastle upon Tyne 1/15/2007 - 1/20/2007
Mathias Drton University of Chicago 1/8/2007 - 3/30/2007
Laurent El Ghaoui University of California 1/18/2007 - 1/19/2007
Richard Falk Rutgers University 1/7/2007 - 1/12/2007
Lingling Fan Midwest ISO 1/12/2007 - 1/13/2007
Lingling Fan Midwest ISO 1/16/2007 - 1/20/2007
Makan Fardad University of Minnesota Twin Cities 8/26/2006 - 8/13/2007
Maryam Fazel California Institute of Technology 1/14/2007 - 1/21/2007
Eric Feron Georgia Institute of Technology 1/15/2007 - 1/20/2007
Lawrence A. Fialkow SUNY at New Paltz 1/15/2007 - 1/20/2007
Stephen E. Fienberg Carnegie-Mellon University 1/1/2007 - 3/31/2007
Pedro Forero University of Minnesota Twin Cities 1/16/2007 - 1/20/2007
Ioannis Fotiou Eidgenössische TH Zürich-Hönggerberg 1/10/2007 - 2/16/2007
Dennice Gayme California Institute of Technology 1/15/2007 - 1/21/2007
Tryphon T. Georgiou University of Minnesota Twin Cities 1/16/2007 - 1/20/2007
Sonja Glavaski Honeywell Systems and Research Center 1/16/2007 - 1/20/2007
Jason E. Gower University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Carlos R. Handy Texas Southern University 1/15/2007 - 1/20/2007
Bernard Hanzon National University of Ireland, University College Cork 1/16/2007 - 1/21/2007
Gloria Haro Ortega University of Minnesota Twin Cities 9/1/2005 - 8/31/2007
Christoph Helmberg Technische Universität Chemnitz-Zwickau 1/15/2007 - 1/21/2007
J. William Helton University of California, San Diego 1/14/2007 - 1/26/2007
Didier Henrion Centre National de la Recherche Scientifique (CNRS) 1/15/2007 - 1/21/2007
Milena Hering University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Christopher Hillar Texas A & M University 1/15/2007 - 1/21/2007
Jean-Baptiste Hiriart-Urruty Université de Toulouse III (Paul Sabatier) 1/15/2007 - 1/21/2007
Sung-Pil Hong Seoul National University 1/16/2007 - 2/1/2007
Serkan Hosten San Francisco State University 1/2/2007 - 2/16/2007
Benjamin J. Howard University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Evelyne Hubert Institut National de Recherche en Informatique Automatique (INRIA) 9/1/2006 - 6/30/2007
Farhad Jafari University of Wyoming 9/1/2006 - 6/30/2007
Amin Jafarian University of Texas 1/12/2007 - 1/20/2007
Anders Nedergaard Jensen Aarhus University 9/6/2006 - 6/30/2007
Steve Kaliszewski Arizona State University 1/7/2007 - 6/30/2007
Tapan Kumar Kar Yokohama National University 1/15/2007 - 1/20/2007
Mordechai Katzman University of Sheffield 1/10/2007 - 5/15/2007
Edward D. Kim University of California 1/11/2007 - 1/20/2007
Si-Jo Kim Andong National University 1/12/2007 - 1/13/2007
Si-Jo Kim Andong National University 1/16/2007 - 1/20/2007
Sunyoung Kim Ewha Womans University 1/14/2007 - 1/20/2007
Henry C. King University of Maryland 1/11/2007 - 1/21/2007
Masakazu Kojima Tokyo Institute of Technology 1/14/2007 - 1/20/2007
Salma Kuhlmann University of Saskatchewan 1/13/2007 - 1/20/2007
Nuri Kundak University of Minnesota Twin Cities 1/16/2007 - 1/20/2007
Song-Hwa Kwon University of Minnesota Twin Cities 8/30/2005 - 8/31/2007
Sanjay Lall Stanford University 1/19/2007 - 1/20/2007
Andrew Lamperski California Institute of Technology 1/15/2007 - 1/21/2007
Jean Bernard Lasserre Centre National de la Recherche Scientifique (CNRS) 1/7/2007 - 2/3/2007
Niels Lauritzen Aarhus University 8/28/2006 - 7/10/2007
Anton Leykin University of Minnesota Twin Cities 8/16/2006 - 8/15/2007
Hstau Liao University of Minnesota Twin Cities 9/2/2005 - 8/31/2007
James Lu Johann Radon Institute for Computational and Applied Mathematics 1/15/2007 - 1/21/2007
Tom Luo University of Minnesota Twin Cities 1/16/2007 - 1/20/2007
Laura Lurati University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Gennady Lyubeznik University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Arash Mafi Corning 1/25/2007 - 1/27/2007
Hannah Markwig University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Thomas Markwig Universität Kaiserslautern 9/1/2006 - 6/30/2007
Scott McCullough University of Florida 1/15/2007 - 1/20/2007
Alexandre Megretski Massachusetts Institute of Technology 1/15/2007 - 1/21/2007
Lisa A. Miller University of Minnesota Twin Cities 1/12/2007 - 1/13/2007
Lisa A. Miller University of Minnesota Twin Cities 1/16/2007 - 1/20/2007
Richard Moeckel University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Uwe Nagel University of Kentucky 9/1/2006 - 6/1/2007
Kristen Nairn St. John's University 1/11/2007 - 1/13/2007
Jiawang Nie University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Edwin O'Shea University of Kentucky 1/11/2007 - 1/15/2007
Antonis Papachristodoulou University of Oxford 1/17/2007 - 1/21/2007
Pablo A. Parrilo Massachusetts Institute of Technology 1/11/2007 - 1/21/2007
Gabor Pataki University of North Carolina 1/14/2007 - 1/20/2007
Helfried Peyrl Automatic Control Laboratory 1/15/2007 - 2/3/2007
Victoria Powers Emory University 1/15/2007 - 1/20/2007
Mihai Putinar University of California 1/7/2007 - 3/24/2007
Jacob Quant University of Minnesota Twin Cities 1/16/2007 - 1/20/2007
Bharath Rangarajan University of Minnesota Twin Cities 1/16/2007 - 1/20/2007
Bharath Rangarajan University of Minnesota Twin Cities 1/12/2007 - 1/13/2007
Seid Alireza Razavi Majomard University of Minnesota Twin Cities 1/16/2007 - 1/20/2007
Ben Recht California Institute of Technology 1/15/2007 - 1/20/2007
Victor Reiner University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Franz Rendl Universität Klagenfurt 1/16/2007 - 1/21/2007
James Renegar Cornell University 1/15/2007 - 1/20/2007
John A. Rhodes University of Alaska 1/7/2007 - 4/7/2007
Jakayla Robbins University of Kentucky 1/11/2007 - 1/14/2007
Joel Roberts University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Marie Rognes University of Oslo 1/10/2007 - 6/30/2007
Philipp Rostalski Eidgenössische TH Zürich-Hönggerberg 1/2/2007 - 2/19/2007
Bjarke Hammersholt Roune Aarhus University 9/12/2006 - 6/30/2007
Marie-Francoise Roy Université de Rennes I 1/15/2007 - 1/21/2007
Christopher Ryan University of British Columbia 1/11/2007 - 1/20/2007
Arnd Scheel University of Minnesota Twin Cities 7/15/2004 - 8/31/2007
Markus Schweighofer Universität Konstanz 1/15/2007 - 1/21/2007
Parikshit Shah Massachusetts Institute of Technology 1/11/2007 - 1/20/2007
Chehrzad Shakiban University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Kartik K. Sivaramakrishnan North Carolina State University 1/15/2007 - 1/20/2007
Aleksandra Slavkovic Pennsylvania State University 1/31/2007 - 3/31/2007
Steven Sperber University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Dumitru Stamate University of Minnesota Twin Cities 1/12/2007 - 1/13/2007
Dumitru Stamate University of Minnesota Twin Cities 1/16/2007 - 1/20/2007
Bernd Sturmfels University of California 1/17/2007 - 1/20/2007
Jie Sun National University of Singapore 1/15/2007 - 1/20/2007
Bridget Eileen Tenner Massachusetts Institute of Technology 1/17/2007 - 1/20/2007
Tamas Terlaky McMaster University 1/15/2007 - 1/20/2007
Rekha R. Thomas University of Washington 1/1/2007 - 3/31/2007
Carl Toews University of Minnesota Twin Cities 9/1/2005 - 8/31/2007
Ufuk Topcu University of California 1/15/2007 - 1/20/2007
Levent Tuncel University of Waterloo 1/15/2007 - 1/20/2007
Victor Vinnikov Ben Gurion University of the Negev 1/15/2007 - 1/26/2007
John Voight University of Minnesota Twin Cities 8/15/2006 - 8/31/2007
Martin J. Wainwright University of California 1/16/2007 - 1/19/2007
Tiyu Wang University of California 1/11/2007 - 1/13/2007
Angelika Wiegele Universität Klagenfurt 1/15/2007 - 1/21/2007
Ragnar Winther University of Oslo 1/7/2007 - 1/12/2007
Henry Wolkowicz University of Waterloo 1/14/2007 - 1/20/2007
Gregory Emmanuel Yawson Lawrence Technological University 1/11/2007 - 1/20/2007
Josephine Yu University of California 1/9/2007 - 6/30/2007
Hongchao Zhang University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Lihong Zhi Chinese Academy of Sciences 1/11/2007 - 3/4/2007
Yuriy Zinchenko McMaster University 1/16/2007 - 1/19/2007
Legend: Postdoc or Industrial Postdoc Long-term Visitor

IMA Affiliates:
3M, Boeing, Carnegie-Mellon University, Corning, ExxonMobil, Ford, General Electric, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Johnson & Johnson, Kent State University, Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Mississippi State University, Motorola, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger-Doll, Schlumberger-Doll Research, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Texas, University of Wisconsin, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute