Abstract. 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 analyze the behavior of pattern search in the neighborhood of an isolated local minimizer. We show that a recognizable subsequence converges r-linearly to the minimizer. Key words. pattern search, local convergence analysis, global convergence analysis, desultory rate of convergence 1. Introduction. Pattern search methods are a class of direct search methods for solving nonlinear optimization problems. The global convergence properties of pattern search for both constrained and unconstrained problems have been established in a series of papers [7] [8] [9] [10] [11] . In this paper, we consider the local convergence properties of pattern search and revisit the global convergence properties in light of these new results. For simplicity, our discussion will focus on the case of unconstrained minimization:
Local convergence properties have been studied later by REF .
On The Local Convergence Of Pattern Search
SIAM Journal on Optimization
Computer Science Mathematics