English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Extragradient method (EG) (Korpelevich, 1976) is one of the most popularmethods for solving saddle point and variational inequalities problems (VIP).Despite its long history and significant attention in the optimizationcommunity, there remain important open questions about convergence of EG. Inthis paper, we resolve one of such questions and derive the first last-iterate$O(1/K)$ convergence rate for EG for monotone and Lipschitz VIP without anyadditional assumptions on the operator unlike the only known result of thistype (Golowich et al., 2020) that relies on the Lipschitzness of the Jacobianof the operator. The rate is given in terms of reducing the squared norm of theoperator. Moreover, we establish several results on the (non-)cocoercivity ofthe update operators of EG, Optimistic Gradient Method, and HamiltonianGradient Method, when the original operator is monotone and Lipschitz.

Extragradient Method: $O(1/K)$ Last-Iterate Convergence for Monotone Variational Inequalities and Connections With Cocoercivity