A scalarization proximal point method for quasiconvex multiobjective minimization

H. C.F. Apolinário; E. A. Papa Quiroz; P. R. Oliveira

doi:10.1007/s10898-015-0367-3

A scalarization proximal point method for quasiconvex multiobjective minimization

H. C.F. Apolinário, E. A. Papa Quiroz, P. R. Oliveira

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, that the sequence generated by the method is well defined and converges globally to a Pareto-Clarke critical point. Our method may be seen as an extension, for nonconvex case, of the inexact proximal method for multiobjective convex minimization problems studied by Bonnel et al. (SIAM J Optim 15(4):953–970, 2005).

Original language	English
Pages (from-to)	79-96
Number of pages	18
Journal	Journal of Global Optimization
Volume	64
Issue number	1
DOIs	https://doi.org/10.1007/s10898-015-0367-3
State	Published - 1 Jan 2016

Bibliographical note

Funding Information:
This research was conducted with partial financial support from CAPES, through the Interagency Doctoral Program New Frontiers UFRJ/UFT. The research of the second author was supported by the Postdoctoral Scholarship CAPES-FAPERJ Edital PAPD-2011.

Funding Information:
The research of H.C.F. Apolinário was partially supported by CAPES/Brazil. The research of P.R.Oliveira was partially supported by CNPQ/Brazil. The research of E.A.Papa Quiroz was partially supported by the Postdoctoral Scholarship CAPES-FAPERJ Edital PAPD-2011.

Publisher Copyright:
© 2015, Springer Science+Business Media New York.

Keywords

Clarke subdifferential
Fejér convergence
Multiobjective minimization
Pareto-Clarke critical point
Proximal point methods
Quasiconvex functions

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10.1007/s10898-015-0367-3

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KW - Fejér convergence

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KW - Proximal point methods

KW - Quasiconvex functions

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A scalarization proximal point method for quasiconvex multiobjective minimization

Abstract

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