Analysis of Generalized Pattern SearchesCharles

This paper contains a new analysis for the Generalized Pattern Search (GPS) methods of Torczon and Lewis and Torczon. The two novel aspects are that the proofs are much shorter, and they use weaker continuity assumptions. Speciically, under very mild conditions, the method nds an interesting limit point even if the objective function is not continuous and is even extended valued. If the objective is Lipschitz near the limit point, then appropriate directional derivatives of the objective are zero. If the objective is strictly diierentiable at the limit point, then the gradient exists and is zero. The results here show the power of GPS on some classes of real problems better than the previous analysis for continuously diierentiable objectives.