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).
Bibliographical noteFunding Information:
The research of H.C.F. Apolin??rio 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. 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.
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- Clarke subdifferential
- Fejér convergence
- Multiobjective minimization
- Pareto-Clarke critical point
- Proximal point methods
- Quasiconvex functions