A Proximal Point-Type Method for Multicriteria Optimization - Aix-Marseille Université Access content directly
Journal Articles Set-Valued and Variational Analysis Year : 2014

A Proximal Point-Type Method for Multicriteria Optimization

Glaydston Carvalho Bento
J.X. Cruz Neto
  • Function : Author

Abstract

In this paper, we present a proximal point algorithm for multicriteria optimization, by assuming an iterative process which uses a variable scalarization function. With respect to the convergence analysis, firstly we show that, for any sequence generated from our algorithm, each accumulation point is a Pareto critical point for the multiobjective function. A more significant novelty here is that our paper gets full convergence for quasi-convex functions. In the convex or pseudo-convex cases, we prove convergence to a weak Pareto optimal point. Another contribution is to consider a variant of our algorithm, obtaining the iterative step through an unconstrained subproblem. Then, we show that any sequence generated by this new algorithm attains a Pareto optimal point after a finite number of iterations under the assumption that the weak Pareto optimal set is weak sharp for the multiobjective problem.
No file

Dates and versions

hal-01463765 , version 1 (09-02-2017)

Identifiers

Cite

Glaydston Carvalho Bento, J.X. Cruz Neto, Antoine Soubeyran. A Proximal Point-Type Method for Multicriteria Optimization. Set-Valued and Variational Analysis, 2014, 22 (3), pp.557--573. ⟨10.1007/s11228-014-0279-2⟩. ⟨hal-01463765⟩
69 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More