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

In this paper, we adapt the control theoretic concept of dissipativity theoryto provide a natural understanding of Nesterov's accelerated method. Our theoryties rigorous convergence rate analysis to the physically intuitive notion ofenergy dissipation. Moreover, dissipativity allows one to efficiently constructLyapunov functions (either numerically or analytically) by solving a smallsemidefinite program. Using novel supply rate functions, we show how to recoverknown rate bounds for Nesterov's method and we generalize the approach tocertify both linear and sublinear rates in a variety of settings. Finally, welink the continuous-time version of dissipativity to recent works on algorithmanalysis that use discretizations of ordinary differential equations.

Dissipativity Theory for Nesterov's Accelerated Method