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

Universidade Federal do Tocantins
Universidad Nacional Mayor de San Marcos
Universidade Federal do Rio de Janeiro

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

30 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
Externally published	Yes

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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title = "A scalarization proximal point method for quasiconvex multiobjective minimization",

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).",

keywords = "Clarke subdifferential, Fej{\'e}r convergence, Multiobjective minimization, Pareto-Clarke critical point, Proximal point methods, Quasiconvex functions",

author = "Apolin{\'a}rio, \{H. C.F.\} and \{Papa Quiroz\}, \{E. A.\} and Oliveira, \{P. R.\}",

note = "Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media New York.",

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AU - Apolinário, H. C.F.

AU - Papa Quiroz, E. A.

AU - Oliveira, P. R.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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).

AB - 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).

KW - Clarke subdifferential

KW - Fejér convergence

KW - Multiobjective minimization

KW - Pareto-Clarke critical point

KW - Proximal point methods

KW - Quasiconvex functions

UR - https://www.scopus.com/pages/publications/84952716031

U2 - 10.1007/s10898-015-0367-3

DO - 10.1007/s10898-015-0367-3

M3 - Article

AN - SCOPUS:84952716031

SN - 0925-5001

VL - 64

SP - 79

EP - 96

JO - Journal of Global Optimization

JF - Journal of Global Optimization

IS - 1

ER -

A scalarization proximal point method for quasiconvex multiobjective minimization

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Keywords

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