Proximal extrapolated gradient methods for variational inequalities

Abstract

The paper concerns with novel first-order methods for monotone variational inequalities. They use a very simple linesearch procedure that takes into account a local information of the operator. Also the methods do not require Lipschitz-continuity of the operator and the linesearch procedure uses only values of the operator. Moreover, when operator is affine our linesearch becomes very simple, namely, it needs only vector-vector multiplication. For all our methods we establish the ergodic convergence rate. Although the proposed methods are very general, sometimes they may show much better performance even for optimization problems. The reason for this is that they often can use larger stepsizes without additional expensive computation.

References in corpus (1)

• A hybrid method without extrapolation step for solving variational inequality problems

Cited by in corpus (6)

• A first-order primal-dual algorithm with linesearch
• Golden Ratio Algorithms for Variational Inequalities
• A golden ratio primal-dual algorithm for structured convex optimization
• First-Order Methods for Optimal Experimental Design Problems with Bound Constraints
• First-order primal-dual algorithm with correction
• Proximal extrapolated gradient methods with prediction and correction for monotone variational inequalities