Pattern Search Algorithms for Mixed Variable General Constrained Optimization Problems

This is a AIR FORCE INST OF TECH WRIGHT-PATTERSONAFB OH report procured by the Pentagon and made available for public release. It has been reproduced in the best form available to the Pentagon. It is not spiral-bound, but rather assembled with Velobinding in a soft, white linen cover. The Storming Media report number is A708604. The abstract provided by the Pentagon follows: A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented The Audet-Dennis Generalized Pattern Search (GPS) algorithm for bound constrained mixed variable optimization problems is extended to problems with general nonlinear constraints by incorporating a filter in which new iterates are accepted whenever they decrease the incumbent objective function value or constraint violation function value Additionally, the algorithm can exploit any available derivative information (or rough approximation thereof) to speed convergence without sacrificing the flexibility often employed by GPS methods to find better local optima. In generalizing existing GPS algorithms, the new theoretical convergence results presented here reduce seamlessly to existing results for more specific classes of problems. While no local continuity or smoothness assumptions are made, a hierarchy of theoretical convergence results is given, in which the assumptions dictate what can be proved about certain limit points of the algorithm. A new Matlab software package was developed to implement these algorithms. Numerical results are provided for several nonlinear optimization problems from the CUTE test set.