Inertial subgradient extragradient method for solving pseudomonotone equilibrium problems and fixed point problems in Hilbert spaces
Zhongbing Xie, Gang Cai, Bing Tan
Abstract
This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.
Topics & Concepts
Subgradient methodHilbert spaceFixed pointMathematicsConvergence (economics)Lipschitz continuityInertial frame of referenceSequence (biology)Applied mathematicsWeak convergenceMathematical optimizationIterative methodAlgorithmComputer scienceMathematical analysisBiologyEconomic growthQuantum mechanicsGeneticsPhysicsEconomicsAsset (computer security)Computer securityOptimization and Variational AnalysisAdvanced Optimization Algorithms ResearchFixed Point Theorems Analysis