Optimization using Surrogates for Engineering Design

John E. Dennis Jr. (email, cv in pdf)
Department of Computational and Applied Mathematics
Rice University

(April 4th, 2002)

Abstract:
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.

The school will consist of 10 one-hour lectures:

• Lectures 1-2: Properties of the target class of problems.
  
  
• Lecture 3: Surrogates for expensive functions.
  
  
• Lecture 4: The surrogate management framework.
  
  
• Lectures 5-7: The barrier generalized pattern search method (GPS) for closed constraints.
  
  
• Lecture 8-10: The filter GPS method for open constraints.

Last updated: April 22nd, 2002 by Luís N. Vicente