A projected subgradient method for solving generalized mixed variational inequalities

Authors:
Fu-Quan Xia;Nan-Jing Huang;Zhi-Bin Liu
Affiliations:
Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610066, PR China;Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China and State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu, 610500, PR China;Department of Applied Mathematics, Southwest Petroleum University, Chengdu, 610500, PR China and State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu, 610500, PR China
Venue:
Operations Research Letters
Year:
2008

Citing 7
Cited 3

Auxiliary problem principle extended to variational inequalities

Journal of Optimization Theory and Applications
Applications of splitting algorithm to decomposition in convex programming and variational inequalities

SIAM Journal on Control and Optimization
Entropy-like proximal methods in convex programming

Mathematics of Operations Research
Family of perturbation methods for variational inequalities

Journal of Optimization Theory and Applications
On the projected subgradient method for nonsmooth convex optimization in a Hilbert space

Mathematical Programming: Series A and B
A New Projection Method for Variational Inequality Problems

SIAM Journal on Control and Optimization
A Bundle Method for Solving Variational Inequalities

SIAM Journal on Optimization

Degree theory for a generalized set-valued variational inequality with an application in Banach spaces

Journal of Global Optimization
An inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities

Computers & Mathematics with Applications
Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the projected subgradient method for solving generalized mixed variational inequalities. In each step, we choose an @e"k-subgradient u^k of the function f and w^k in a set-valued mapping T, followed by an orthogonal projection onto the feasible set. We prove that the sequence is weakly convergent.