Sequential and parallel algorithms for global minimizing functions with Lipschitzian derivatives

In this paper, sequential and parallel algorithms using derivatives for solving unconstrained one-dimensional global optimization problems are described. Sufficient conditions of convergence to all global minimizers are established for both methods. Parallel algorithm conditions, which guarantee significant speed up in comparison to the sequential version of the method, are presented. The sequential method is numerically compared with the algorithms of Breiman and Cutler, Pijavskii, and Strongin on a set of 20 test functions taken from literature. We also present results of numerical experiments illustrating the performance of the parallel method. All experiments have been executed on the parallel computer ALLIANT FX/80.