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

Nonconvex and nonsmooth optimization problems are important and challengingfor statistics and machine learning. In this paper, we propose ProjectedProximal Gradient Descent (PPGD) which solves a class of nonconvex andnonsmooth optimization problems, where the nonconvexity and nonsmoothness comefrom a nonsmooth regularization term which is nonconvex but piecewise convex.In contrast with existing convergence analysis of accelerated PGD methods fornonconvex and nonsmooth problems based on the Kurdyka-\L{}ojasiewicz (K\L{})property, we provide a new theoretical analysis showing local fast convergenceof PPGD. It is proved that PPGD achieves a fast convergence rate of$\cO(1/k^2)$ when the iteration number $k \ge k_0$ for a finite $k_0$ on aclass of nonconvex and nonsmooth problems under mild assumptions, which islocally Nesterov's optimal convergence rate of first-order methods on smoothand convex objective function with Lipschitz continuous gradient. Experimentalresults demonstrate the effectiveness of PPGD.

Projective Proximal Gradient Descent for A Class of Nonconvex Nonsmooth  Optimization Problems: Fast Convergence Without Kurdyka-Lojasiewicz (KL)  Property