A refined proximal algorithm for nonconvex multiobjective optimization in Hilbert spaces

G. C. Bento (), J. X. Cruz Neto (), J. O. Lopes (), B. S. Mordukhovich () and P. R. Silva Filho ()
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G. C. Bento: Federal University of Goiás
J. X. Cruz Neto: Federal University of Piauí
J. O. Lopes: Federal University of Piauí
B. S. Mordukhovich: Wayne State University
P. R. Silva Filho: Federal University of Piauí

Journal of Global Optimization, 2025, vol. 92, issue 1, No 8, 187-203

Abstract: Abstract This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on limiting/Mordukhovich 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 providing its detailed convergence analysis. The obtained results largely extend those initiated by Bonnel et al. [SIAM J Optim, 15 (2005), pp. 953–970] for convex vector optimization problems, specifically in the case where the codomain is an m-dimensional space and by Bento et al. [SIAM J Optim, 28 (2018), pp. 1104-1120] for nonconvex finite-dimensional problems in terms of Clarke’s generalized gradients.

Keywords: Multiobjective programming; Proximal point algorithm; Locally lipschitz-continuous functions; Weakly pareto point (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-024-01453-6

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