Journal of the Operations Research Society of China ›› 2017, Vol. 5 ›› Issue (4): 545-561.doi: 10.1007/s40305-017-0156-4

Special Issue: Continuous Optimization

• Continuous Optimization • Previous Articles    

An Inexact Proximal Method with Proximal Distances for Quasimonotone Equilibrium Problems

Lennin Mallma Ramirez1 · Erik Alex Papa Quiroz1,2 ·P. R. Oliveira1   

  1. 1 Coordenação dos Programas de Pós-gaduação em Engenharia- Programa de Engenharia de Sistemas e Computação, Federal University of Rio de Janeiro, Rio of Janeiro, Brazil
    2 Mayor de San Marcos National University, Lima, Peru
  • Online:2017-12-30 Published:2017-12-30
  • Supported by:

    L. Mallma Ramirez’s research was supported by Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior(CAPES). The research of the E. A. Papa Quiroz was supported by the Postdoctoral Scholarship CAPES-Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (No. EditalPAPD-2011), and P. R.Oliveira’s research was partially supported by Conselho Nacional de Desemvolvimento Científico e Tecnológico.

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Abstract:

In this paper, we propose an inexact proximal point method to solve equilibrium problems using proximal distances and the diagonal subdifferential. Under some natural assumptions on the problem and the quasimonotonicity condition on the bifunction, we prove that the sequence generated by the method converges to a solution point of the problem.

Key words: Equilibrium problems ·, Quasimonotonicity ·, Proximal distance ·Proximal method

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