MULTIDIMENSIONAL BISECTION APPLIED TO GLOBAL OPTIMIZATION

A family of deterministic algorithms is introduced, designed to solve the global optimisation problem for Lipschitz continuous functions of many variables. All the algorithms can be considered as generalisations of the bisection method: they proceed via a sequence of brackets whose infinite intersection is the set of global optima. Brackets are unions of similar simplexes. Acceleration methods, convergence properties and optimality questions are considered.