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

• An algorithm for multidimensional bi-objective Lipschitz optimization is proposed.
• The algorithm is based on branch-and-bound approach and trisection of hyper-rectangles.
• The bounding fronts are based on Lipschitz conditions for objective functions.
• Numerical examples are included.

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.