Analysis of Generalized Pattern Search
John DennisRice University
Thursday, May 29th, 3.00 p.m. CERFACS Conference Room
Abstract :
We present a new analysis for the Generalized Pattern Search methods of Torczon and Lewis and Torczon. The two novel aspects are that the proofs are much shorter, and they use weaker smoothness assumptions. Specifically, we identify interesting limit points even if the objective function is not continuous or finite valued. If the objective is Lipschitz near the limit point, then appropriate directional derivatives of the objective are nonnegative. If the objective is strictly differentiable at the limit point, then the gradient exists and is zero.
These results show the power of Generalized Pattern Search on some classes of real problems better than the previous analysis for continuously differentiable objectives.
We provide a similar analysis for a new derivative-free algorithm for general nonlinear programming. Our new algorithm combines pattern search step choice with filter algorithms for step acceptance. Roughly, a filter method accepts a step that either improves the objective function value or the value of some function that measures the constraint violation.
This work is joint with Charles Audet.
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