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arXiv · 2403.09922

A Refined Proximal Algorithm for Nonconvex Multiobjective Optimization in Hilbert Spaces

G. C. Bento·J. X. Cruz Neto·J. O. Lopes·B. S. Mordukhovich·P. R. Silva Filho
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Abstract

This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Pareto critical points for such problems, establish necessary optimality conditions for them, and then employ these conditions to develop a refined version of the vectorial proximal point algorithm with providing its detailed convergence analysis. The obtained results largely extend those initiated by Bonnel, Iusem and Svaiter \cite{Bonnel2005} for convex vector optimization problems and by Bento et al. \cite{Bento2018} for nonconvex finite-dimensional problems in terms of Clarke's generalized gradients.

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G. C. Bento, J. X. Cruz Neto, J. O. Lopes, B. S. Mordukhovich, P. R. Silva Filho. 2024-03-14. A Refined Proximal Algorithm for Nonconvex Multiobjective Optimization in Hilbert Spaces. https://arxiv.org/abs/2403.09922

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