Evolutionary pattern search algorithms for unconstrained and linearly constrained optimization

We describe a convergence theory for evolutionary pattern search algorithms (EPSA) on a broad class of unconstrained and linearly constrained problems. EPSA adaptively modify the step size of the mutation operator in response to the success of previous optimization steps. The design of EPSA is inspired by recent analyzes of pattern search methods. Our analysis significantly extends the previous convergence theory for EPSA. Our analysis applies to a broader class of EPSA and it applies to problems that are nonsmooth, have unbounded objective functions, and are linearly constrained. Further, we describe a modest change to the algorithmic framework of EPSA for which a nonprobabilistic convergence theory applies. These analyses are also noteworthy because they are considerably simpler than previous analyses of EPSA.