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An inexact scalarized proximal algorithm with quasi- distance for convex and quasiconvex multi-objective minimization

Erik Papa Quiroz(erikpapa***at***gmail.com)
Rogério Rocha(azevedo***at***uft.edu.br)
Paulo Oliveira(poliveir***at***cos.ufrj.br)
Gregório Ronaldo(rgregor***at***ufrrj.br)

Abstract: In the paper of Rocha et al., J Optim Theory Appl (2016) 171:964979, the authors introduced a proximal point algorithm with quasi-distances to solve unconstrained convex multi-objective minimization problems. They proved that all accumulation points are ecient solutions of the problem. In this pa- per we analyze an inexact proximal point algorithm to solve convex and qua- siconvex unconstrained multi-objective minimization problems using quasi- distances. For the convex case, we extend the result obtained by the exact algorithm of Rocha et al. and for the quasiconvex case we prove that all ac- cumulation points are Pareto-Clarke critical points of the problem. Finally, to show the practicality of the introduced algorithm, we present numerical examples that con rm the convergence of our algorithm.

Keywords: Proximal point algorithm - Multi-objective minimization - Effcient solutions - Quasi-distance - Pareto-Clarke critical points

Category 1: Nonlinear Optimization

Category 2: Other Topics (Multi-Criteria Optimization )


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Entry Submitted: 04/01/2020
Entry Accepted: 04/01/2020
Entry Last Modified: 04/01/2020

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