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/

Zendy Plus

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

Zendy Tools

Zendy Open

Primal-dual splitting schemes are a class of powerful algorithms that solvecomplicated monotone inclusions and convex optimization problems that are builtfrom many simpler pieces. They decompose problems that are built from sums,linear compositions, and infimal convolutions of simple functions so that eachsimple term is processed individually via proximal mappings, gradient mappings,and multiplications by the linear maps. This leads to easily implementable andhighly parallelizable or distributed algorithms, which often obtain nearlystate-of-the-art performance. In this paper, we analyze a monotone inclusionproblem that captures a large class of primal-dual splittings as a specialcase. We introduce a unifying scheme and use some abstract analysis of thealgorithm to prove convergence rates of the proximal point algorithm,forward-backward splitting, Peaceman-Rachford splitting, andforward-backward-forward splitting applied to the model problem. Our ergodicconvergence rates are deduced under variable metrics, stepsizes, andrelaxation. Our nonergodic convergence rates are the first shown in theliterature. Finally, we apply our results to a large class of primal-dualalgorithms that are a special case of our scheme and deduce their convergencerates.

Convergence rate analysis of primal-dual splitting schemes