Korpelevich's method for variational inequality problems in Banach spaces

Authors:
Alfredo N. Iusem;Mostafa Nasri
Affiliations:
Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil CEP 22460-320;Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil CEP 22460-320
Venue:
Journal of Global Optimization
Year:
2011

Citing 11
Cited 2

Parallel and distributed computation: numerical methods

Parallel and distributed computation: numerical methods
Modification of the extra-gradient method for solving variational inequalities and certain optimization problems

USSR Computational Mathematics and Mathematical Physics
A new method for a class of linear variational inequalities

Mathematical Programming: Series A and B
Modified Projection-Type Methods for Monotone Variational Inequalities

SIAM Journal on Control and Optimization
Convergence Properties of Feasible Descent Methods for Solving Variational Inequalities in Banach Spaces

Computational Optimization and Applications
A New Projection Method for Variational Inequality Problems

SIAM Journal on Control and Optimization
Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems

SIAM Journal on Optimization
Interior projection-like methods for monotone variational inequalities

Mathematical Programming: Series A and B
Solution continuity in variational conditions

Journal of Global Optimization
A differential game of joint implementation of environmental projects

Automatica (Journal of IFAC)
On generalized Nash games and variational inequalities

Operations Research Letters

Korpelevich's method for variational inequality problems on Hadamard manifolds

Journal of Global Optimization
A new iterative scheme for a countable family of relatively nonexpansive mappings and an equilibrium problem in Banach spaces

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose a variant of Korpelevich's method for solving variational inequality problems with operators in Banach spaces. A full convergence analysis of the method is presented under reasonable assumptions on the problem data.