Dual extragradient algorithms extended to equilibrium problems

Authors:
Tran D. Quoc;Pham N. Anh;Le D. Muu
Affiliations:
Hanoi University of Science, Hanoi, Vietnam and Department of Electrical Engineering (ESAT/SCD) and OPTEC, K.U. Leuven, Leuven, Belgium;Posts and Telecommunications Institute of Technology, Hanoi, Vietnam;Institute of Mathematics, Hanoi, Vietnam
Venue:
Journal of Global Optimization
Year:
2012

Citing 10
Cited 0

Auxiliary problem principle extended to variational inequalities

Journal of Optimization Theory and Applications
Convergence of an adaptive penalty scheme for finding constrained equilibria

Nonlinear Analysis: Theory, Methods & Applications
An extended descent framework for variational inequalities

Journal of Optimization Theory and Applications
Equilibrium programming using proximal-like algorithms

Mathematical Programming: Series A and B
Gap Functions for Equilibrium Problems

Journal of Global Optimization
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming

Mathematical Programming: Series A and B
Dual extrapolation and its applications to solving variational inequalities and related problems

Mathematical Programming: Series A and B
Structured Prediction, Dual Extragradient and Bregman Projections

The Journal of Machine Learning Research
A bundle method for solving equilibrium problems

Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
The interior proximal extragradient method for solving equilibrium problems

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we propose two iterative schemes for solving equilibrium problems which are called dual extragradient algorithms. In contrast with the primal extragradient methods in Quoc et al. (Optimization 57(6):749---776, 2008) which require to solve two general strongly convex programs at each iteration, the dual extragradient algorithms proposed in this paper only need to solve, at each iteration, one general strongly convex program, one projection problem and one subgradient calculation. Moreover, we provide the worst case complexity bounds of these algorithms, which have not been done in the primal extragradient methods yet. An application to Nash-Cournot equilibrium models of electricity markets is presented and implemented to examine the performance of the proposed algorithms.