The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem

G. Bento, J. Cruz Neto, G. López, Antoine Soubeyran and J. Souza
Additional contact information
G. Bento: UFG - Universidade Federal de Goiás [Goiânia]
J. Cruz Neto: UFPI - Universidade Federal do Piauí
G. López: Universidad de Sevilla = University of Seville
J. Souza: UFPI - Universidade Federal do Piauí, UFRJ - Universidade Federal do Rio de Janeiro [Brasil] = Federal University of Rio de Janeiro [Brazil] = Université fédérale de Rio de Janeiro [Brésil]

Post-Print from HAL

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.

Date: 2018-01
Note: View the original document on HAL open archive server: https://amu.hal.science/hal-01985333
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Published in SIAM Journal on Optimization, 2018, 28 (2), pp.1104-1120. ⟨10.1137/16M107534X⟩

Downloads: (external link)
https://amu.hal.science/hal-01985333/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01985333

DOI: 10.1137/16M107534X

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().