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Winter 2003
IMA Short Course
Industrial Strength Optimization
January 6-7, 2003

Optimization, September 2002 - June 2003


Mark A. Abramson, Maj, USAF
Department of Mathematics and Statistics
Air Force Institute of Technology

Charles Audet
Departement de Mathematiques et de Genie Industry
Ecole Polytechnique de Montreal

John Dennis
Department of Computational and Applied Mathematics
Rice University

Material for the 4 Lectures:
IMALec1.pdf IMALec1print.pdf
IMALec2.pdf IMALec2print.pdf
IMALec3.pdf IMALec3.ps
IMALec3print.pdf IMALec3print.ps
IMALec4.pdf IMALec4print.pdf

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:
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
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
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
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.


As of 1/7/2003
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