CRPC-TR99785						February 1999

Title: Pattern Search Algorithms for Mixed Variable Programming

Authors: Charles Audet and J.E. Dennis Jr.

Submitted February 1999

Abstract:
Generalized pattern search methods for solving
nonlinear bound constrained optimization problems are extended
here to mixed continuous and discrete variables. The notion of
local optimality in mixed variable programming is defined through
a user-specified set of neighboring points.  We present a
generalized pattern search algorithm that provides accumulation
points that satisfy some appropriate necessary conditions for
local optimality. These points are the limits of subsequences of
unsuccessful iterates whose corresponding mesh size parameters
converge to zero. We present a stronger, more expensive, version
of the algorithm that guarantees additional necessary optimality
conditions. A small example illustrates the differences between
the two versions.  A larger example shows promise for the class of
algorithms suggested here.

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Charles Audet		J.E. Dennis Jr.
charlesa@caam.rice.edu	dennis@caam.rice.edu
Department of Computational and Applied Mathematics
Rice University