The University of Southampton
University of Southampton Institutional Repository

A convergent iterative hard thresholding for nonnegative sparsity optimization

A convergent iterative hard thresholding for nonnegative sparsity optimization
A convergent iterative hard thresholding for nonnegative sparsity optimization
The iterative hard thresholding (IHT) algorithm is a popular greedy-type method in (linear and nonlinear) compressed sensing and sparse optimization problems.
In this paper, we give an improved iterative hard thresholding algorithm for solving the nonnegative sparsity optimization (NSO) by employing the Armijo-type stepsize rule, which automatically adjusts the stepsize and support set and leads to a sufficient decrease of the objective function each iteration.
Consequently, the improved IHT algorithm enjoys several convergence properties under standard assumptions. Those include the convergence to $\alpha$-stationary point (also known as $L$-stationary point in literature if the objective function has Lipschitz gradient) and the finite identification of the true support set. We also characterize when the full sequence converges to a local minimizer of NSO and establish its linear convergence rate. Extensive numerical experiments are included to demonstrate the good performance of the proposed algorithm.
sparsity constrained optimization
1348-9151
325-353
Pan, Lili
9e19dd08-99c8-47b4-ace4-0f4de73efe61
Zhou, Shenglong
d183edc9-a9f6-4b07-a140-a82213dbd8c3
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Pan, Lili
9e19dd08-99c8-47b4-ace4-0f4de73efe61
Zhou, Shenglong
d183edc9-a9f6-4b07-a140-a82213dbd8c3
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85

Pan, Lili, Zhou, Shenglong, Xiu, Naihua and Qi, Hou-Duo (2017) A convergent iterative hard thresholding for nonnegative sparsity optimization. Pacific Journal of Optimization, 13 (2), 325-353.

Record type: Article

Abstract

The iterative hard thresholding (IHT) algorithm is a popular greedy-type method in (linear and nonlinear) compressed sensing and sparse optimization problems.
In this paper, we give an improved iterative hard thresholding algorithm for solving the nonnegative sparsity optimization (NSO) by employing the Armijo-type stepsize rule, which automatically adjusts the stepsize and support set and leads to a sufficient decrease of the objective function each iteration.
Consequently, the improved IHT algorithm enjoys several convergence properties under standard assumptions. Those include the convergence to $\alpha$-stationary point (also known as $L$-stationary point in literature if the objective function has Lipschitz gradient) and the finite identification of the true support set. We also characterize when the full sequence converges to a local minimizer of NSO and establish its linear convergence rate. Extensive numerical experiments are included to demonstrate the good performance of the proposed algorithm.

Text
CIHT - Accepted Manuscript
Download (502kB)

More information

Accepted/In Press date: 21 February 2017
Published date: May 2017
Keywords: sparsity constrained optimization
Organisations: Mathematical Sciences, Operational Research

Identifiers

Local EPrints ID: 408654
URI: http://eprints.soton.ac.uk/id/eprint/408654
ISSN: 1348-9151
PURE UUID: 233cd7bc-edf9-4d1e-8970-decd59cacf4f
ORCID for Shenglong Zhou: ORCID iD orcid.org/0000-0003-2843-1614
ORCID for Hou-Duo Qi: ORCID iD orcid.org/0000-0003-3481-4814

Catalogue record

Date deposited: 25 May 2017 04:03
Last modified: 30 Jul 2020 01:46

Export record

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×