Random Search Methods with Multiple Search Points

Similar to the multi-start procedures in mathematical programming, here we consider random search methods working with multiple search variates (points) at an iteration point. The probability of failure, success, resp., and their properties at an iteration point are then evaluated for conditional independent, i.i.d., resp, stochastic search points. Furthermore, reachability results are given, i.e., results on the probability to reach an \(\epsilon \) -optimal point with increasing stage or time. Finally, an optimized search process is studied based on the search point with minimum function value among all successful search points at the current iteration point.