Journal articles
The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem
Abstract : This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel, Iusem, and Svaiter [SIAM J. Optim., 15 (2005), pp. 953--970] is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new (scalarization-free) approach for convergence analysis of the method is proposed where the first-order optimality condition of the scalarized problem is replaced by a necessary condition for weak Pareto points of a multiobjective problem. As a consequence, this has allowed us to consider the method without any assumption of convexity over the constraint sets that determine the vectorial improvement steps. This is very important for applications; for example, to extend to a dynamic setting the famous compromise problem in management sciences and game theory.
https://hal-amu.archives-ouvertes.fr/hal-01985333
Contributor : Elisabeth Lhuillier Connect in order to contact the contributor
Submitted on : Tuesday, February 1, 2022 - 5:41:54 PM
Last modification on : Thursday, February 3, 2022 - 3:39:55 AM
Long-term archiving on: : Tuesday, May 3, 2022 - 8:51:22 AM
Contributor : Elisabeth Lhuillier Connect in order to contact the contributor
Submitted on : Tuesday, February 1, 2022 - 5:41:54 PM
Last modification on : Thursday, February 3, 2022 - 3:39:55 AM
Long-term archiving on: : Tuesday, May 3, 2022 - 8:51:22 AM
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Compromise PB SIAMOPT.pdf
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