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

Authors:
Arkadi Nemirovski
Affiliations:
-
Venue:
SIAM Journal on Optimization
Year:
2005

Citing 0
Cited 23

Solving fractional packing problems in Oast(1/ε) iterations

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound

Foundations and Trends in Signal Processing
Mining brain region connectivity for alzheimer's disease study via sparse inverse covariance estimation

Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Accuracy Certificates for Computational Problems with Convex Structure

Mathematics of Operations Research
A Quasi-Newton Approach to Nonsmooth Convex Optimization Problems in Machine Learning

The Journal of Machine Learning Research
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm

ACM Transactions on Algorithms (TALG)
Smoothing Techniques for Computing Nash Equilibria of Sequential Games

Mathematics of Operations Research
Exploiting redundancy for aerial image fusion using convex optimization

Proceedings of the 32nd DAGM conference on Pattern recognition
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging

Journal of Mathematical Imaging and Vision
Korpelevich's method for variational inequality problems in Banach spaces

Journal of Global Optimization
lp-Norm Multiple Kernel Learning

The Journal of Machine Learning Research
On the Complexity of the Hybrid Proximal Extragradient Method for the Iterates and the Ergodic Mean

SIAM Journal on Optimization
On the $O(1/n)$ Convergence Rate of the Douglas-Rachford Alternating Direction Method

SIAM Journal on Numerical Analysis
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
Optimizing over the growing spectrahedron

ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Accelerated Linearized Bregman Method

Journal of Scientific Computing
A double smoothing technique for solving unconstrained nondifferentiable convex optimization problems

Computational Optimization and Applications
Sparse non Gaussian component analysis by semidefinite programming

Machine Learning
Trading regret for efficiency: online convex optimization with long term constraints

The Journal of Machine Learning Research
Efficient methods for robust classification under uncertainty in kernel matrices

The Journal of Machine Learning Research
An improved first-order primal-dual algorithm with a new correction step

Journal of Global Optimization
On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose a prox-type method with efficiency estimate $O(\epsilon^{-1})$ for approximating saddle points of convex-concave C$^{1,1}$ functions and solutions of variational inequalities with monotone Lipschitz continuous operators. Application examples include matrix games, eigenvalue minimization, and computing the Lovasz capacity number of a graph, and these are illustrated by numerical experiments with large-scale matrix games and Lovasz capacity problems.