ON OPTIMIZATION USING SURROGATES FOR ENGINEERING DESIGN
May 8-11 2002, Coimbra, Portugal
Optimization using Surrogates for Engineering Design
John E. Dennis Jr. (email,
cv in pdf)
Department of Computational and Applied Mathematics
(April 4th, 2002)
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
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