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Journal of Global Optimization

, Volume 64, Issue 1, pp 79–96 | Cite as

A scalarization proximal point method for quasiconvex multiobjective minimization

  • H. C. F. ApolinárioEmail author
  • E. A. Papa Quiroz
  • P. R. Oliveira
Article

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

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

Notes

Acknowledgments

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.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Undergraduate Computation Sciences CourseFederal University of TocantinsPalmasBrazil
  2. 2.Department of Ciencias MatemáticasMayor de San Marcos National UniversityLimaPeru
  3. 3.Computing and Systems Engineering DepartmentFederal University of Rio de JaneiroRio de JaneiroBrazil

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