A ONE-DIMENSIONAL DETERMINISTIC GLOBAL MINIMIZATION ALGORITHM

A new sequential algorithm for solving one-dimensional global optimization problems without limitations for the objective function with unknown Lipschitz constant is described. This method operates using adaptive estimates of local Lipschitz constants in subintervals of the search region. The conditions for global convergence of the algorithm are given and the conditions which guarantee the better behaviour of the algorithm than those of Pijavskii and Strongin and the passive algorithm are derived theoretically. The conditions for the stability of the method are presented. The algorithm is compared(for 20 problems from the literature) with the methods of Gal'perin, Pijavskii and Strongin and with the passive algorithm.