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

We leverage the connections between nonexpansive maps, monotone Lipschitzoperators, and proximal mappings to obtain near-optimal (i.e., optimal up topoly-log factors in terms of iteration complexity) and parameter-free methodsfor solving monotone inclusion problems. These results immediately translateinto near-optimal guarantees for approximating strong solutions to variationalinequality problems, approximating convex-concave min-max optimizationproblems, and minimizing the norm of the gradient in min-max optimizationproblems. Our analysis is based on a novel and simple potential-based proof ofconvergence of Halpern iteration, a classical iteration for finding fixedpoints of nonexpansive maps. Additionally, we provide a series of algorithmicreductions that highlight connections between different problem classes andlead to lower bounds that certify near-optimality of the studied methods.

Halpern Iteration for Near-Optimal and Parameter-Free Monotone Inclusion and Strong Solutions to Variational Inequalities