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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


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 extendedvalued 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 standalone solvers for partial differential equations, table lookups, 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.
MONDAY,
JANUARY 6 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 


9:3010:00 am  Coffee 
Reception Room EE/CS 3176 
10:0011:30 am  John Dennis  Optimization Using Surrogates for Engineering Design pdf 
2:003:30 pm  Charles Audet  Generalized Pattern Search Algorithms: Unconstrained and Constrained Cases pdf 
TUESDAY,
JANUARY 7 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:3010:00 am  Coffee  Reception Room EE/CS 3176 
10:0011:30 am  Mark A. Abramson  Direct Search Methods for Categorical Variables 
2:003:30 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.
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  SchlumbergerDoll 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 
JeongSoo 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  SchlumbergerDoll Research 