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

Perspective functions arise explicitly or implicitly in various forms inapplied mathematics and in statistical data analysis. To date, no systematicstrategy is available to solve the associated, typically nonsmooth,optimization problems. In this paper, we fill this gap by showing that proximalmethods provide an efficient framework to model and solve problems involvingperspective functions. We study the construction of the proximity operator of aperspective function under general assumptions and present important instancesin which the proximity operator can be computed explicitly or viastraightforward numerical operations. These results constitute central buildingblocks in the design of proximal optimization algorithms. We showcase theversatility of the framework by designing novel proximal algorithms forstate-of-the-art regression and variable selection schemes in high-dimensionalstatistics.

Perspective Functions: Proximal Calculus and Applications in High-Dimensional Statistics