Efficiency of a Global Optimization Algorithm

An algorithm forr determining the global minimum of an unconstrained function f is considered. The algorithm is due to Skelboe, Moore, Asaithambe and Shen. The method is applicable to functions f having so-called inclusion functions. Such inclusion functions are easily found using some simple features of interval arithmetic. The convergence conditions of the algorithm were studied by Ratschek [16], where it was shown that assumptions like continuity, convexity, bounded number of global or local minimizers, etc., can be dropped. present paper continues the investigations of the algorithm and presents sharp estimates for the convergence order. The order depends polynomially on the size of the domain of f and exponentially on the order of the inclusion function chosen and the dimension of the problem.