A Linear Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization

Erik Alex Papa Quiroz, Hellena Christina Fernandes Apolinário, Kely Diana Villacorta, Paulo Roberto Oliveira

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper, we propose a linear scalarization proximal point algorithm for solving lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and, using the condition that the proximal parameters are bounded, we prove the convergence of the sequence generated by the algorithm and, when the objective functions are continuous, we prove the convergence to a generalized critical point of the problem. Furthermore, for the continuously differentiable case we introduce an inexact algorithm, which converges to a Pareto critical point.

Original languageEnglish
Pages (from-to)1028-1052
Number of pages25
JournalJournal of Optimization Theory and Applications
Volume183
Issue number3
DOIs
StatePublished - 1 Dec 2019
Externally publishedYes

Bibliographical note

Funding Information:
The authors thank the referees for their helpful comments and suggestions. The research of the first author was supported by the Postdoctoral Scholarship CAPES-FAPERJ Edital PAPD-2011. The research of P.R.Oliveira was partially supported by CNPQ/Brazil.

Funding Information:
The authors thank the referees for their helpful comments and suggestions. The research of the first author was supported by the Postdoctoral Scholarship CAPES-FAPERJ Edital PAPD-2011. The research of P.R.Oliveira was partially supported by CNPQ/Brazil.

Keywords

  • Fejér convergence
  • Lower semicontinuous quasiconvex functions
  • Multiobjective minimization
  • Pareto–Clarke critical point
  • Proximal point methods

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