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 language | English |
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Pages (from-to) | 1028-1052 |
Number of pages | 25 |
Journal | Journal of Optimization Theory and Applications |
Volume | 183 |
Issue number | 3 |
DOIs | |
State | Published - 1 Dec 2019 |
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.
Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Fejér convergence
- Lower semicontinuous quasiconvex functions
- Multiobjective minimization
- Pareto–Clarke critical point
- Proximal point methods