An efficient descent method for locally Lipschitz multiobjective optimization problems

Abstract

In this article, we present an efficient descent method for locally Lipschitz continuous multiobjective optimization problems (MOPs). The method is realized by combining a theoretical result regarding the computation of descent directions for nonsmooth MOPs with a practical method to approximate the subdifferentials of the objective functions. We show convergence to points which satisfy a necessary condition for Pareto optimality. Using a set of test problems, we compare our method to the multiobjective proximal bundle method by Mäkelä. The results indicate that our method is competitive while being easier to implement. While the number of objective function evaluations is larger, the overall number of subgradient evaluations is lower. Finally, we show that our method can be combined with a subdivision algorithm to compute entire Pareto sets of nonsmooth MOPs.

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Cited by in corpus (4)

• On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation
• Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models
• A note on the convergence of deterministic gradient sampling in nonsmooth optimization
• Analyzing the speed of convergence in nonsmooth optimization via the Goldstein subdifferential with application to descent methods