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HOME » PROGRAMS/ACTIVITIES » Annual Thematic Program
IMA Short Course
Industrial Strength Optimization
Speakers:
Mark
A. Abramson,
Maj, USAF
Department of Mathematics and Statistics
Air Force Institute of Technology
Mark.Abramson@afit.edu
Charles
Audet
Departement de Mathematiques et de Genie Industry
Ecole Polytechnique de Montreal
charles.audet@gerad.ca
John Dennis
Department of Computational and Applied Mathematics
Rice University
dennis@caam.rice.edu
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| IMALec1.pdf | IMALec1print.pdf |
| IMALec2.pdf | IMALec2print.pdf |
| IMALec3.pdf | IMALec3.ps |
| IMALec3print.pdf | IMALec3print.ps |
| IMALec4.pdf | IMALec4print.pdf |
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The goal of these lectures is to acquaint the audience with a class of nasty optimization problems involving nonconvex nonlinear extended-valued functions. Such functions arise often in multidisciplinary optimization (MDO). The context for applying our algorithms determines the form of the algorithms, and to present this context requires a bit more than just a short list of assumptions. Briefly though, the objective function and constraints depend not only on the optimization variables, but also on some ancillary variables such as the solutions of some coupled systems of stand-alone solvers for partial differential equations, table look-ups, and other nonsmooth simulation codes. This has important algorithmic implications: First, the function and constraint values may be very expensive. Second, the functions may be nondifferentiable and discontinuous. In fact, they are often treated as extended valued since a function call may not return a value even if all the specified constraints are satisfied.
The approach we take in these lectures has been successful for some real problems in engineering design. We hope to convince engineers and mathematicians alike that not only are the algorithms given here useful, but the mathematics involved is interesting and relevant. We hope to convince mathematicians that good applied problems produce good mathematics, and that contrary to what they may have heard, they will suffer no loss of virtue as a direct result of considering them.
This course will consist of 4 lectures of 1.5 hours each:
| MONDAY,
JANUARY 6 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted. |
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| 9:30-10:00 am | Coffee |
Reception Room EE/CS 3-176 |
| 10:00-11:30 am | John Dennis | Optimization Using Surrogates for Engineering Design pdf |
| 2:00-3:30 pm | Charles Audet | Generalized Pattern Search Algorithms: Unconstrained and Constrained Cases pdf |
| TUESDAY,
JANUARY 7 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted. |
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| 9:30-10:00 am | Coffee | Reception Room EE/CS 3-176 |
| 10:00-11:30 am | Mark A. Abramson | Direct Search Methods for Categorical Variables |
| 2:00-3:30 pm | John Dennis | Surrogate Management Framework pdf |
Breakdown of the 4 Lectures: (slides)
Lecture 1. MDO: Multidisciplinary Optimization is a contextual framework in which to view a large class of important optimization applications. MDO is the name used in aerospace but this class of problems is also called "optimization of linked subsystems" in the DOE community, and "systems of systems" in the military operations research community. This lecture will present a context in which to view various MDO formulations, including the one we will concentrate on in this shortcourse.
Lectures 2&3. Direct Search Methods: These two lectures will present algorithms and some analysis for an important subclass of MDO problems that arise in engineering design. The particular format presented allows the use of surrogates to lessen the number of expensive simulation calls needed to drive the optimization. This format will be used for algorithms with simple linear constraints, nonlinear constraints, and categorical variables. In addition, ways will be given to use poor derivative information to increase efficiency, when that information is available.
Lecture 4. Surrogate Optimization: This lecture will show how the algorithmic framework presented in the previous two lectures gives rise to the surrogate management framework. Numerical results will be given the surrogate management framework applied to some industrial design problems.
LIST OF CONFIRMED PARTICIPANTS
| Name | Department | Affiliation |
|---|---|---|
| Mark Abramson | Mathematics and Statics | Air Force Institute of Technology |
| Oleg Alexandrov | Mathematics | University of Minnesota |
| Montaz Ali | Computational and Applied Mathematics | Witwatersrand University |
| Yusuf Bilgin Altundas | Schlumberger-Doll Research | |
| Charles Audet | Departement de Mathematiques et de Genie Indust. | Ecole Polytechnique de Montreal |
| Olga Brezhneva | Institute for Mathematics and its Applications | University of Minnesota |
| Dongwei Cao | Computer Science | University of Minnesota |
| Jamylle Carter | Mathematics | University of Minnesota |
| Collette Coullard | Industrial Eng. & Mgmt. Sciences | Northwestern University |
| Bob Crone | Mechanical R&D | Seagate Technology |
| Dacian Daescu | University of Minnesota | Institute for Mathematics and its Applications |
| John Dennis | Computational & Applied Mathematics | Rice University |
| Grant Erdmann | Mathematics | University of Minnesota |
| Lisa Evans | IMA | University of Minnesota |
| Robert Gulliver | Mathematics | University of Minnesota |
| Herve Kerivin | IMA | University of Minnesota |
| Daniel Kerm | University of Minnesota | Institute for Mathematics and its Applications |
| Tamara Gibson Kolda | Sandia National Laboratories | |
| Maher Lahmar | Industrial Engineering | University of Minnesota |
| Mitch Luskin | Mathematics | University of Minnesota |
| Vamsi Krishna Mareddy | Electrical Engineering | University of Minnesota |
| Alison Marsden | Mechanical Engineering - FPC | Stanford University |
| Wade Martinson | Process Solutions Technology Development Center | Cargill, Inc. |
| Thanasak Mouktonglang | Mathematics | University of Notre Dame |
| Peh Ng | IMA | University of Minnesota |
| Jeong-Soo Park | Statistics | Chonnam National University, Korea |
| Samuel Patterson | Mathematics and Computer Science | Carleton College |
| Samuel Patterson | Mathematics and Computer Science | Carleton College |
| Paul Sacks | Mathematics | Iowa State University |
| M. Nuri Sendil | Industrial Eng. & Mgmt. Sciences | Northwestern University |
| Jing Wang | Institute for Mathematics and its Application | University of Minnesota |
| Todd Wittman | Mathematics | University of Minnesota |
| Jun Zhao | Schlumberger-Doll Research |
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