Analysis of Generalized Pattern Searches

Abstract. This paper contains a new convergence analysis for the Lewis and Torczon GPS class of pattern search methods for linearly constrained optimization. The analysis is motivated by the desire to understand the behavior of the algorithm under hypotheses more consistent with properties satisfied in practice for a class of problems, discussed at various points in the paper, for which these methods are successful. Specifically, even if the objective function is discontinuous or extended valued, the methods find a limit point with some minimizing properties. Simple examples show that the strength of the optimality conditions at a limit point does not depend only on the algorithm, but also on the directions it…

• UA
  U.S. Air Force