Weak convergence of a modified subgradient extragradient algorithm for monotone variational inequalities in Banach spaces

Abstract

Applying the generalized projection operator, we introduce a modified subgradient extragradient algorithm in Banach spaces for a variational inequality involving a monotone Lipschitz continuous mapping which is more general than an inversestrongly-monotone mapping. Weak convergence of the iterative algorithm is also proved. An advantage of the algorithm is the computation of only one value of the inequality mapping and one projection onto the admissible set per one iteration.

A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces

“…The set of the solutions of the variational inequality (1) is denoted by V I(C, A). Lots of problems in physics, optimization, differential equation (inclusion), finance and minimax problem reduce to find an element of (1) and relevant numerical analysis methods can be considered to solve the problems, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”