Year: 2022
Type: preprint
Abstract: We describe a procedure to compute a projection of $w \in \mathbb{R}^n$ into the intersection of the so-called \emph{zero-norm} ball $k \mathbb{B}_0$ of radius $k$, i.e., the set of $k$-sparse vectors, with a box centered at a point of $k \mathbb{B}_0$. The need for such projection arises in the context of certain trust-region methods for nonsmooth regularized optimization. Although the set into which we wish to project is nonconvex, we show that a solution may be found in $O(n \log(n))$ operations. We describe our Julia implementation and illustrate our procedure in the context of two trust-region methods for nonsmooth regularized optimization.
Source: arXiv (Cornell University)
Author: Orban, Dominique
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4223456510