On the Local Convergence of Pattern Search
Elizabeth D. Dolan, Robert Michael Lewis, Virginia J. Torczon · SIAM Journal on Optimization · 2003
We examine the local convergence properties of pattern search methods, complementing the previously established global convergence properties for this class of algorithms. We show that the step-length control parameter which appears in the definition of pattern search algorithms provides a reliable asymptotic measure of first-order stationarity. This gives an analytical justification for a traditional stopping criterion for pattern search methods. Using this measure of first-order stationarity, we both revisit the global convergence properties of pattern search and analyze the behavior of pattern search in the neighborhood of an isolated local minimizer.