Dual extrapolation and its applications to solving variational inequalities and related problems

Authors:
Yurii Nesterov
Affiliations:
Catholic University of Louvain (UCL), Center for Operations Research and Econometrics (CORE), 34 voie du Roman Pays, 1348, Louvain-la-Neuve, Belgium
Venue:
Mathematical Programming: Series A and B
Year:
2007

Citing 0
Cited 6

A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science

SIAM Journal on Imaging Sciences
On the Complexity of the Hybrid Proximal Extragradient Method for the Iterates and the Ergodic Mean

SIAM Journal on Optimization
Dual extragradient algorithms extended to equilibrium problems

Journal of Global Optimization
Iterative methods for solving monotone equilibrium problems via dual gap functions

Computational Optimization and Applications
Complexity of Variants of Tseng's Modified F-B Splitting and Korpelevich's Methods for Hemivariational Inequalities with Applications to Saddle-point and Convex Optimization Problems

SIAM Journal on Optimization
Sparse non Gaussian component analysis by semidefinite programming

Machine Learning

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we suggest new dual methods for solving variational inequalities with monotone operators. We show that with an appropriate step-size strategy, our method is optimal both for Lipschitz continuous operators ($$O({1 \over \epsilon})$$ iterations), and for the operators with bounded variations ($$O({1 \over \epsilon^2})$$ iterations). Our technique can be applied for solving non-smooth convex minimization problems with known structure. In this case the worst-case complexity bound is $$O({1 \over \epsilon})$$ iterations.