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

This paper is intended to solve the nonconvex $\ell_{p}$-ball constrainednonlinear optimization problems. An iteratively reweighted method is proposed,which solves a sequence of weighted $\ell_{1}$-ball projection subproblems. Ateach iteration, the next iterate is obtained by moving along the negativegradient with a stepsize and then projecting the resulted point onto theweighted $\ell_{1}$ ball to approximate the $\ell_{p}$ ball. Specifically, ifthe current iterate is in the interior of the feasible set, then the weighted$\ell_{1}$ ball is formed by linearizing the $\ell_{p}$ norm at the currentiterate. If the current iterate is on the boundary of the feasible set, thenthe weighted $\ell_{1}$ ball is formed differently by keeping those zerocomponents in the current iterate still zero. In our analysis, we prove thatthe generated iterates converge to a first-order stationary point. Numericalexperiments demonstrate the effectiveness of the proposed method.

An Iteratively Reweighted Method for Sparse Optimization on Nonconvex $\ell_{p}$ Ball