Details

Autor(en) / Beteiligte

• Gebken, Bennet
• Peitz, Sebastian

Titel

An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems

Ist Teil von

• Journal of optimization theory and applications, 2021-03, Vol.188 (3), p.696-723

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2021

Link zum Volltext

Quelle

SpringerLink

Beschreibungen/Notizen

• We present an efficient descent method for unconstrained, locally Lipschitz multiobjective optimization problems. The method is realized by combining a theoretical result regarding the computation of descent directions for nonsmooth multiobjective optimization problems 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 with the multiobjective proximal bundle method by Mäkelä. The results indicate that our method is competitive while being easier to implement. Although the number of objective function evaluations is larger, the overall number of subgradient evaluations is smaller. Our method can be combined with a subdivision algorithm to compute entire Pareto sets of nonsmooth problems. Finally, we demonstrate how our method can be used for solving sparse optimization problems, which are present in many real-life applications.