Parallel Asynchronous Global Search and the Nested Optimization Scheme

In this paper, a parallel asynchronous information algorithm for solving multidimensional Lipschitz global optimization problems, where times for evaluating the objective function can be different from point to point, is proposed. This method uses the nested optimization scheme and a new parallel asynchronous global optimization method for solving core univariate subproblems generated by the nested scheme. The properties of the scheme related to parallel computations are investigated. Global convergence conditions for the new method and theoretical conditions of speed up, which can be reached by using asynchronous parallelization in comparison with the pure sequential case, are established. Numerical experiments comparing sequential, synchronous, and asynchronous algorithms are also reported.