Two New Inertial Algorithms for Solving Variational Inequalities in Reflexive Banach Spaces
Simeon Reich, Truong Minh Tuyen, Pongsakorn Sunthrayuth, Prasit Cholamjiak
Abstract
The purpose of this paper is to introduce and analyze two inertial algorithms with self-adaptive stepsizes for solving variational inequalities in reflexive Banach spaces. Our algorithms are based on inertial hybrid and shrinking projection methods. Knowledge of the Lipschitz constant of the cost operator is not required. Under appropriate conditions, the strong convergence of the algorithms is established. We also present several numerical experiments which bring out the efficiency and the advantages of the proposed algorithms. Our work provides extensions of many known results from Hilbert spaces to reflexive Banach spaces.
Topics & Concepts
MathematicsBanach spaceVariational inequalityInertial frame of referenceHilbert spaceLipschitz continuityPseudo-monotone operatorConvergence (economics)ReflexivityAlgorithmPure mathematicsApplied mathematicsFinite-rank operatorOperator spaceSociologyEconomicsQuantum mechanicsPhysicsSocial scienceEconomic growthOptimization and Variational AnalysisTopology Optimization in EngineeringContact Mechanics and Variational Inequalities