Main navigation  Main content
Complete List of Industrial Postdoc Seminar
The IMA Postdoc Seminar is intended for expository talks from the visitors on their current research interests. For the year 2002  2003 it is organized by Miaojung Yvonne Ou and Olga Brezhneva.



 






May
20 (Tuesday) 11:15 am 12:15 pm Room 409, Lind Hall 
Speaker: Don Aronson, Director of Postdoctoral Program in the IMA Title: Transmission in Inhomogeneous Excitable Media Abstract: In the first part of the talk, I will review some aspects of the transmission of signals in a homogeneous excitable medium such as a nerve axon. There is a hierarchy of mathematical models ranging from the ultra precise (and Nobel Prize worthy) HodgkinHuxley system to the McKeanFitzHughNagumo caricature. I will be mostly concerned with the latter. The second part of the talk will be a highly speculative discussion of what happens to transmission when one introduces inhomogeneities in the form of passive gaps. The object here is to pose some potentially interesting problems. 


May
13 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Beth Allen, Professor of Economics, University of Minnesota Title: Some Theoretical Approaches to Product Development Abstract: This talk will survey some recent research focusing on the early stages of the product life cycle: Design (choice of product or product line) and manufacturing (in contrast to the later stages in the supply chain of, for instance, scheduling, distribution, inventory strategy, postpurchase service/maintenance/repair, and endoflife reuse/recycling/disposal). First, the mathematical structure of the design space (in particular, for homogeneous geometric objects or shapes, so that the set of potential product designs consists of equivalence classes of nonempty closed subsets of a Euclidean space), will be examined. Implications for constrained optimization will be analyzed. Relations to quality control and manufacturing will be considered. 


April
22 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Luis Goddyn, Mathematics, Simon Fraser University Title: The WorstCase Euclidean Traveling Salesman Problem Abstract: How should a finite set X of points be arranged within a finite region R in Euclidean dspace, so as to maximize the length L(X) of a TSP tour through X? It turns out that, if the size n of X is large, then the shape of R becomes irrelevant, and if R has unit volume, then the assymptotic growth is L(X) _{d} n^{(d1) /d} (_{d} depends only on the dimension d). We discuss methods and issues involved in estimating the value of the fundamental coefficient _{d}. This talk involves a mix of geometry, sphere packing, quantizers, heuristics and algorithm analysis. 


April
15 (Tuesday) 11:15 am 12:15 pm Room 409, Lind Hall 
Speaker: Douglas N. Arnold, IMA Director Title: Talking Math to People Who Don't Know Any Abstract: Mathematicians are often criticizedby themselves and othersfor being incapable of describing their work to nonmathematicians. In this seminar I will discuss ways to communicate mathematics to the public using as a case study a talk I gave recently on optimization for the IT Quarterly, a "forum for friends of the Institute of Technology." 


April
1 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Tamon Stephen, IMA Postdoctoral Associate Title: The LiftandProject Approach to Integer Programs Abstract: In this survey talk, we discuss the ``lift and project'' approach for solving 01 integer programs. Our main example is the method of semidefinite matrix relaxations proposed by Lovasz and Schrijver. 


March
25 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: C. Roos, Delft University of Technology, Netherlands and IMA visitor, March 2003 Title: What is special with the logarithmic barrier function in optimization? Slides: pdf Abstract: After its introduction by Frisch in 1955, the logarithmic barrier function (LBF) has played a major role in the field optimization. The revolutionary developments of the past two decades in this field, which gave rise to the subfield of interiorpoints (IP) methods, has reemphasized its importance. The search directions in all stateoftheart IPsolvers for linear, and also for secondorder cone and semidefinite optimization problems are explicitly or implicitly based on an LBF, and the analysis of these methods strongly depends on properties of such functions. Other barrier functions have been proposed, but both from a theoretical and computational viewpoint LBF's always were winning, at least surviving. It has often been asked what makes LBF so special. In this talk we deal with this question. We focus on primaldual methods for linear optimization. It is probably for the first time that alternative barrier functions have been found that in some cases provide better theoretical complexity results than the LBF. The results can be extended to other conic optimization problems; it is an open question if the new barrier functions can be adapted to primal methods and dual methods, respectively. This is joint work with Y. Bai (Shanghai University, China) and M. Elghami (Delft University of Technology, Netherlands). 




March
4 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Toshio Yoshikawa, IMA Postdoctoral Associate Title: Toda Lattice Type Model for Nonlinear Viscoelastic Material Abstract: Viscoelastic materials are materials which behave like elastic body in short time scale and like liquid in long time scale. In this talk I will discuss a mathematical model of viscoelastic materials. The model I propose here is based on Toda lattice. Toda lattice is an onedimensional chain of nonlinear springs with exponential type force function; it is one of few known integrable mechanical systems. A remarkable feature of Toda lattice is that it has a family of exact solutions called solitons; these are solitary waves traveling at constant velocity along the lattice. I will modify Toda lattice to include viscoelasticity and discuss solitons on this modified lattice. As part of this talk, I will give the introduction to the solitons on the original Toda lattice. 


February
25 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Luis N. Vicente, Department of Mathematics, University of Coimbra, Portugal IBM T.J. Watson Research Center, Yorktown Heights, New York and IMA, University of Minnesota Title: Space Mapping: Models, Algorithms and Applications Abstract: A number of new techniques have been developed to deal with optimization problems which involve expensive function evaluations from simulation or experimentation. One of the techniques that has been recently considered in the engineering community is the socalled spacemapping approach. Space mapping assumes the existence of two models for the same physical phenomenon: a fine model, accurate and expensive, and a coarse model, significantly cheaper and considerably less accurate. The idea behind space mapping is to "construct" a mapping between the finemodel space of parameters or variables and the coarsemodel space that allows to defer the optimization process to the coarse model, where most function evaluations should take place. Spacemapping techniques are typically iterative as the mapping is unknown a priori and it is calculated for a sequence of points in the fine space. One of the goals of this talk is to organize some of the model and algorithmic aspects of space mapping in a mathematical framework which allows us to look at the properties of the space mapping and to fit the convergence analysis of the algorithms into the existence convergence theory of nonlinear optimization. We will also introduce new ways of building the space mapping and deriving the algorithms. We will report recent numerical testing with the application of the spacemapping methodology to optimal control problems governed by partial differential equations. We will show how the space mapping technique can be used in the context of this class of problems. This is joint work with Michael Hintermuller. 


February
18 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Moritz Diehl, University of Heidelberg, Germany & IMA visitor JanuaryMarch 2003 Title: Nominal Stability for Nonlinear Model Predictive Control Abstract: Nonlinear Model Predictive Control (NMPC) is a technique for the design of feedback controllers that works by online minimization of an objective depending on the predicted system behaviour. Typically, the system shall be kept in some desired steady state, and the objective penalizes deviations from it. A basic requirement for the resulting feedback controller is that it stabilizes the system at the given operating point at least in the case that the model is perfect  this property is called nominal stability. In the talk, I will introduce the basic ideas underlying the standard stability proofs for NMPC. I will shortly discuss how the stability problem changes if numerical optimization errors are taken into account, and give a sketch of recent results to address this problem. 


February
11 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Peh Ng, Dept of Mathematics, University of Minnesota  Morris & IMA Visitor 20022003 Title: A Commodity Family Extended Formulation Approach to Solving Uncapacitated Fixed Charge Network Flow Problems Abstract: In general, uncapacitated fixed charge network flow problem, (UF), is NPHard. However, previous research on a few NPHard problems has shown that improved linear programming relaxations can be obtained by using extended reformulations. In this research, we develop a theory of extended formulations for (UF) by reformulating these problems in terms of an extended variable set corresponding to flow commodities defined by arbitrary demand subsets. In particular, we show how to produce an extended formulation for any suitable commodity family and isolate simple axioms characterizing the families that yield the most useful reformulations. 


February
4 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Michael J.D. Powell, University of Cambridge Title: Radial Basis Function Methods for Global Optimization 


January
28 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: John Dennis, Rice University and the IMA Title: Working With Industry or My Life as an Evangelist Abstract: In this talk, I will discuss my work with various industrial groups, including my first real experience as a consultant to the National Bureau of Economic Research starting in the early `70s. I will try to explain the research each collaboration motivated and how it affected my work with graduate students. I will also try to draw some conclusions on how to collaborate successfully with industrial or semiindustrial groups  in case you might want to try it. My hope is to convince you that you can do interesting work and help the rather dismal image of mathematicians by seeking such collaborations yourself. To this end, there will not be many technical details, and I hope for an interactive presentation rather than a lecture. 


January
21 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Dacian N. Daescu, IMA Postdoctoral Associate Title: Adjointbased Techniques for the Analysis of Largescale Uncertain Systems Abstract: Despite the increased complexity in the model representations, it is often the case that comprehensive dynamical models show poor results when compared to observational data. To address this problem we need to consider various factors that may contribute to the uncertainties in the analysis of dynamical systems. Data assimilation techniques (e.g. Kalman filter, variational methods) combine observations of a dynamical system with a dynamical model of the system to provide an optimal estimate of the evolving state of the system. In fourdimensional variational data assimilation (4DVar) a minimization algorithm is used to find the set of control variables such that an optimal fit between the model forecast and observations, scattered in time, is achieved. For largescale models, the minimization of the cost functional is a very intensive computational process. At the same time, the development and validation of dynamical models require a systematic sensitivity analysis to evaluate the effects of parameter variations on model prediction. The adjoint modeling is presented as an efficient tool to evaluate the sensitivity of a scalar response function with respect to initial conditions and model parameters. Using the adjoint method, the necessary gradient may be computed at the expense of few function evaluations, making the optimization process very efficient. The sensitivity field obtained through a single backward integration of the adjoint model may be used to identify parameters that play an essential role in determining the model forecast. The intimate connection between measurements and models can be illustrated through the example of largescale field experiments. The difficulty in planning such experiments lies in the fact that the features of interest are usually transient in nature. Expensive fielddeployed resources (facilities and people) can be employed/utilized more effectively and science success can be maximized by an optimal allocation of the observational resources. The problem of optimal deployment of additional observational resources is presented and adjointbased adaptive observations strategies using the singular value decomposition and gradient sensitivity are discussed in detail. Numerical illustrations are shown for nonlinear chemical reactions systems and atmospheric circulation models. 


December
3 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Maurice Queyranne, Professor of Management Science, Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, Canada Title:
On Optimum SizeConstrained Set Partitions with Submodular
Costs 


November
26 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Lili Ju, IMA Industrial Postdoc Title: Some Topics on Centroidal Voronoi Tessellations Centroidal Voronoi tessellations (CVT) are Voronoi tessellations of a region such that the generating points of the tessellations arealso the centroids of the corresponding Voronoi regions. Such tessellations and their extension for general surfaces are of use in very diverse applications, including data compression, clustering analysis, cell biology, territorial behavior of animals, optimal allocation of resources, grid generations and optimization, meshless computing, and interpolation. Some detreminstic and probabilistic algorithms for computing CVTs will also be discussed. 


November
19 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Marshall Hampton, NSF Postdoctoral Fellow, School of Mathematics, U of M Title: Celestial Mechanics: Recent Progress and Open Problems Abstract: In the last few years there have been some exciting developments in celestial mechanics. A new type of orbit (a "choreography") in the 3body problem was discovered which leads to many open questions. The study of relative equilibria in the nbody problem has blossomed and led to applications in energy efficient orbits for interplanetary spacecraft. Several weeks ago a solution was announced for the simplest case of a longstanding conjecture ("Saari's Conjecture") in the 3body problem. An attempt will be made to survey some of these results, applications, and open problems. 


November
5 (Tuesday) 2:15 am3:15 pm Room 409, Lind Hall 
Speaker: Michael Ball, R H Smith School of Business and Institute for Systems Research University of Maryland Title:
Mathematical Models for Supporting AvailabletoPromise
(ATP) Abstract: The Available to Promise (ATP) business function is the set of capabilities that support responding to customer order requests. Traditionally ATP refers to a simple database lookup into the Master Production Schedule. With the advent of ebusiness, maketoorder production and high variety product offerings, ATP functionality has become a critical component of many business? strategies and also now requires much more complex model and IT support. In this talk, we provide an overview of ATPrelated research and of ATP business practice. We classify ATP research into two categories: pushbased models, which allocate resources and prepare information based on forecasted demand and pullbased models, which generate responses to actual customer orders. A variety of relevant research will be covered, including mixed integer programming models for resource allocation, stochastic models of uncertain customer demand, online scheduling algorithms for generating order delivery dates and strategies for searching for available inventory. 


October
29 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Daniel Kern, IMA Postdoctoral Associate Title: Multispecies Competition and Traveling Waves Abstract: The consideration of spatial factors in ecological modeling has led to a variety of interesting problems in the current literature. Besides better explaining the development of biological phenomena, the resulting models can lead to interesting mathematics. Here, the spread of two invasive plant species and the corresponding replacement of a single native species is examined as a competition model with spatial considerations. The general model is a system of three nonlinear reactiondiffusion equations of the LotkaVolterra type. A model is developed for a specific case involving cottonwoods and two invasive plants in New Mexico. The existence of a traveling wave solution is then examined, leading to possible restrictions on the propagation speed of the exotic species. 


October
22 (Tuesday) 11:15am12:15 pm Room 409, Lind Hall 
Speaker: Lisa Evans, IMA Postdoctoral Associate Title: An Overview of Gomory's Group Approach to Solving Integer Programs Abstract: This talk will give an overview of Gomory's group approach to solving integer programs, including some of the key theorems. It will also describe how facets of master cyclic group problems can be used to generate cutting planes for general IP's. A related method that generates cutting planes from piecewiselinear subadditive functions that approximate the facets of master cyclic group problems will also be presented. Some new classes of facets for the master cyclic group problem will be described, as well as preliminary computational results using subadditive functions to generate cutting planes. 


October
17 (Thursday) 3:154:05 pm Lecture Hall EE/CS 3180 
Speaker: Igor Vasilév,Universite di Salerno, Italy/ Institute of System Dynamics and Control Theory, Russia Title: Computational Experience with LargeScale pMedian Problems Abstract: Given a directed graph, the pMedian problem consist of determining p nodes (the median nodes) minimizing the total distance to the other nodes of the graph. We present a BranchandCut algorithm yielding provably good solutions for instances up to 3795 nodes of complete graphs, proving in most the cases their optimality. The key ingredients of our approach are: lagrangian relaxation, a simple procedure to choose the "promising variables," preprocessing, a columnandrow generation strategy to solve LPrelaxation, cutting planes. 


October
8 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Miaojung Yvonne Ou, IMA Title: Object Inverse Scattering in an Ocean with Sloping Seabed Abstract: This talk considers an obstacle inverse scattering problem in a sloping seabed. The incident waves are sent from point sources along a straight line parallel to the sea surface, and the corresponding scattered fields are measured from a line above the unknown object. We prove a uniqueness theorem for the inverse problem, and describe a generalized dual space indicator method for numerical solution. Numerical results will be presented. 


October
1 (Tuesday) 11:15 am12:15 pm Room 409, Lind Hall 
Speaker: Professor Mike Siddoway, Colorado College (Visiting scholar in School of Math., UMN) Title: RModules with the KrullSchmidt Property Abstract: A fundamental question mathematicians ask is whether a given structure decomposes in a nice way. For instance, in the ring of integers we know that any number can be written uniquely as a product of primes. If we expand the integers in some simple way we sometimes lose uniqueness. We also know that any finite dimensional vector space is completely characterized by its dimension. That is, there is only one way to write a vector space (up to isomorphism) as a direct sum of indecomposable vector spaces. The indecomposable vector spaces are simply the one dimensional vector spaces. An Rmodule is just a vector space with the scalar field replaced by a commutative ring. An abelian group can be viewed as a Zmodule, a module over the integers. In module theory, we say that a class of modules has the KrullSchmidt Property if every module in the class is uniquely (up to isomorphism) the direct sum of indecomposable members of the class. By our earlier comments we see that finite dimensional vector spaces have the KrullSchmidt Property. This idea was first formulated by Krull in the 20's for finite groups. In this talk I will explore decompositions of modules with some finiteness conditions over various rings, and say a few things about when these modules have the KrullSchmidt Property. 