A novel hybrid method for equilibrium problems and fixed point problems

2015/10/28 by Dang Van Hieu, Van Hieu, Dang
Computer Science · Mathematics · #65K10 #65K15 #90C33 #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.OC #msc:65K10 #msc:65K15 #msc:90C33

paper · pdf · doi:10.48550/arxiv.1510.08441

11 pages (submitted). arXiv admin note: substantial text overlap with arXiv:1510.08201; text overlap with arXiv:1510.08217

arxiv created 2015/10/28 · openalex publication_date 2015/10/28 · arxiv updated 2015/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the extra-steps as in some previously known methods. The strongly convergence theorem is established and some numerical examples are presented to illustrate its convergence.

Citations

• Monotone Operators and the Proximal Point Algorithm
• Bilevel Optimization as a Regularization Approach to Pseudomonotone Equilibrium Problems
• An extension of hybrid method without extrapolation step to equilibrium problems
• Hybrid algorithms without the extra-steps for equilibrium problems

Related

• Hybrid algorithms without the extra-steps for equilibrium problems
• An extension of hybrid method without extrapolation step to equilibrium problems
• A strong convergence theorem for solving an equilibrium problem and a fixed point problem using the Bregman distance
• Weak convergence theorems for a symmetric generalized hybrid mapping and an equilibrium problem
• Weak convergence theorems for equilibrium problems and generalized Hybrid mappings