A Self-Adaptive Step Size Algorithm for Solving Variational Inequalities with the Split Feasibility Problem with Multiple Output Sets Constraints
Tran Luu Cuong, Tran Viet Anh, Lê Huỳnh Mỹ Vân
Abstract
In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split feasibility problem with multiple output sets in real Hilbert spaces. The strong convergence of the proposed algorithm is proved without knowing any information of the Lipschitz and strongly monotone constants of the mapping. In addition, the implementation of the algorithm does not require the computation or estimation of the norms of the given bounded linear operators. Special cases are considered. Finally, a numerical experiment has been carried out to illustrate the proposed algorithm.
Topics & Concepts
MathematicsVariational inequalityMonotone polygonHilbert spaceLipschitz continuityConvergence (economics)Bounded functionComputationAlgorithmStrongly monotoneSet (abstract data type)Applied mathematicsMathematical optimizationPure mathematicsMathematical analysisComputer scienceGeometryProgramming languageEconomicsEconomic growthOptimization and Variational AnalysisContact Mechanics and Variational InequalitiesAdvanced Optimization Algorithms Research