SINGLE PROJECTION ALGORITHM FOR VARIATIONAL INEQUALITIES IN BANACH SPACES WITH APPLICATION TO CONTACT PROBLEM

作     者：Yekini SHEHU Yekini SHEHU

作者机构：Department of MathematicsZhejiang Norrmal UniversityJinhua 321004China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2020年第40卷第4期

页      面：1045-1063页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：variational inequality 2-uniformly convex Banach space Tseng’s algorithm strong convergence rate of convergence 

摘      要：We study the single projection algorithm of Tseng for solving a variational inequality problem in a 2-uniformly convex Banach *** underline cost function of the variational inequality is assumed to be monotone and Lipschitz continuous.A weak convergence result is obtained under reasonable assumptions on the variable *** also give the strong convergence result for when the underline cost function is strongly monotone and Lipchitz *** this strong convergence case,the proposed method does not require prior knowledge of the modulus of strong monotonicity and the Lipschitz constant of the cost function as input parameters,rather,the variable step-sizes are diminishing and *** asymptotic estimate of the convergence rate for the strong convergence case is also *** completeness,we give another strong convergence result using the idea of Halpern iteration when the cost function is monotone and Lipschitz continuous and the variable step-sizes are bounded by the inverse of the Lipschitz constant of the cost ***,we give an example of a contact problem where our proposed method can be applied.