Winter 2003

IMA Short Course:

Industrial Strength Optimization

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.

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

Optimization, September 2002 - June 2003