Adaptation of a one-step worst-case optimal univariate algorithm of bi-objective Lipschitz optimization to multidimensional problems

摘要

A bi-objective optimization problem with Lipschitz objective functions is considered. An algorithm is developed adapting a univariate one-step optimal algorithm to multidimensional problems. The univariate algorithm considered is a worst-case optimal algorithm for Lipschitz functions. The multidimensional algorithm is based on the branch-and-bound approach and trisection of hyper-rectangles which cover the feasible region. The univariate algorithm is used to compute the Lipschitz bounds for the Pareto front. Some numerical examples are included. (C) 2014 Elsevier B.V. All rights reserved.