Modified Tseng's splitting algorithms for the sum of two monotone operators in Banach spaces
Jun Yang, Prasit Cholamjiak, Pongsakorn Sunthrayuth
Abstract
<abstract> In this work, we introduce two modified Tseng's splitting algorithms with a new non-monotone adaptive step size for solving monotone inclusion problem in the framework of Banach spaces. Under some mild assumptions, we establish the weak and strong convergence results of the proposed algorithms. Moreover, we also apply our results to variational inequality problem, convex minimization problem and signal recovery, and provide several numerical experiments including comparisons with other related algorithms. </abstract>
Topics & Concepts
Monotone polygonBanach spaceMathematicsVariational inequalityConvergence (economics)Regular polygonConvex optimizationAlgorithmPseudo-monotone operatorMinificationStrongly monotoneDiscrete mathematicsPure mathematicsApplied mathematicsMathematical optimizationFinite-rank operatorGeometryOperator spaceEconomicsEconomic growthOptimization and Variational AnalysisSparse and Compressive Sensing TechniquesNumerical methods in inverse problems