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

Proximal point algorithms have found numerous applications in the field ofconvex optimization, and their accelerated forms have also been proposed.However, the most commonly used accelerated proximal point algorithm was firstintroduced in 1967, and recent studies on accelerating proximal pointalgorithms are relatively scarce. In this paper, we propose high-resolutionODEs for the proximal point operators for both closed proper convex functionsand maximally monotone operators, and present a Lyapunov function framework todemonstrate that the trajectories of our high-resolution ODEs exhibitaccelerated behavior. Subsequently, by symplectically discretizing ourhigh-resolution ODEs, we obtain new proximal point algorithms known assymplectic proximal point algorithms. By decomposing the continuous-timeLyapunov function into its elementary components, we demonstrate thatsymplectic proximal point algorithms possess $O(1/k^2)$ convergence rates.

Symplectic Discretization Approach for Developing New Proximal Point Algorithms