On the performance of pure adaptive search

Studies the pure adaptive search (PAS), an iterative optimization algorithm whose next solution is chosen to be uniformly distributed over the set of feasible solutions that are no worse than the current solution. We extend the results of Patel, Smith and Zabinsky (1988) and Zabinsky and Smith (1992). In particular, we (1) show that PAS converges to the optimal solution almost certainly, (2) show that each PAS iteration reduces the expected remaining feasible-region volume by 50%, and (3) improve the Patel, Smith and Zabinsky complexity measure for convex problems