A survey on proximal point type algorithms for solving vector optimization problems

SM Grad - Splitting Algorithms, Modern Operator Theory, and …, 2019 - Springer
In this survey paper we present the existing generalizations of the proximal point method
from scalar to vector optimization problems, discussing some of their advantages and …

A modified proximal point method for DC functions on Hadamard manifolds

YT Almeida, JX da Cruz Neto, PR Oliveira… - Computational …, 2020 - Springer
We study the convergence of a modified proximal point method for DC functions in
Hadamard manifolds. We use the iteration computed by the proximal point method for DC …

Proximal algorithm with quasidistances for multiobjective quasiconvex minimization in Riemannian manifolds

EAP Quiroz, RA Rocha, P Oliveira… - RAIRO-Operations …, 2023 - rairo-ro.org
We introduce a proximal algorithm using quasidistances for multiobjective minimization
problems with quasiconvex functions defined in arbitrary Riemannian manifolds. The reason …

Approximate efficient solutions of the vector optimization problem on Hadamard manifolds via vector variational inequalities

G Ruiz-Garzón, R Osuna-Gómez, A Rufián-Lizana… - Mathematics, 2020 - mdpi.com
This article has two objectives. Firstly, we use the vector variational-like inequalities
problems to achieve local approximate (weakly) efficient solutions of the vector optimization …

Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm

GC Bento, JX Cruz Neto, LV Meireles… - Annals of Operations …, 2022 - Springer
In this paper we introduce a definition of approximate Pareto efficient solution as well as a
necessary condition for such solutions in the multiobjective setting on Riemannian …

[PDF][PDF] UMA MODIFICAÇÃO NO MÉTODO DO PONTO PROXIMAL PARA FUNÇÕES DC EM VARIEDADES DE HADAMARD

YT Almeida - 2021 - cos.ufrj.br
Na grande maioria dos casos, problemas de otimização envolvem minimizar (ou maximizar)
funções de uma ou mais variáveis em um determinado domínio. Visando resolver esse tipo …

[PDF][PDF] Journal of Nonlinear Analysis and Optimization

S Park - Journal of Nonlinear Analysis and Optimization: Theory …, 2022 - ph03.tci-thaijo.org
This is to give a short history of our multimap classes K, KC, KO in the KKM theory. We show
that many authors adopted or imitated the inadequate definition of the KKM class due to …