Extragradient algorithms for split equilibrium problem and nonexpansive mapping

2015/08/20 by Bui Van Dinh, Van Dinh, Bui, Dang Xuan Son +3
Computer Science · Mathematics · #47H09 #47J25 #65K10 #65K15 #90C99 #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1508.04914

openalex publication_date 2015/08/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose new extragradient algorithms for solving a split equilibrium and nonexpansive mapping SEPNM(C, Q, A, f, g, S, T) where C, Q are nonempty closed convex subsets in real Hilbert spaces H₁, H₂ respectively, A : H₁ → H₂ is a bounded linear operator, f is a pseudomonotone bifunction on C and g is a monotone bifunction on Q, S, T are nonexpansive mappings on C and Q respectively. By using extragradient method combining with cutting techniques, we obtain algorithms for the problem. Under certain conditions on parameters, the iteration sequences generated by the algorithms are proved to be weakly and strongly convergent to a solution of this problem.

Related

• A splitting algorithm for fixed points of nonexpansive mappings and equilibrium problems
• Extragradient algorithms for equilibrium problems and symmetric\n generalized hybrid mappings
• Splitting gradient algorithms for solving monotone equilibrium problems
• Split common fixed point problems and its variant forms
• A shrinking projection approximant for the split equilibrium problems and fixed point problems in Hilbert spaces