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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This note is devoted to the splitting algorithm proposed by Davis and Yin in2017 for computing a zero of the sum of three maximally monotone operators,with one of them being cocoercive. We provide a direct proof that guaranteesits convergence when the stepsizes are smaller than four times the cocoercivityconstant, thus doubling the size of the interval established by Davis and Yin.As a by-product, the same conclusion applies to the forward-backward splittingalgorithm. Further, we use the notion of "strengthening" of a set-valuedoperator to derive a new splitting algorithm for computing the resolvent of thesum. Last but not least, we provide some numerical experiments illustrating theimportance of appropriately choosing the stepsize and relaxation parameters ofthe algorithms.

A direct proof of convergence of Davis-Yin splitting algorithm allowing larger stepsizes