The non-convex sparse problem with nonnegative constraint for signal reconstruction
type: Item
instance of: scholarly article
title: The non-convex sparse problem with nonnegative constraint for signal reconstruction
zbMATH Open document ID: 1353.65058
author: Guanglu Zhou
author: Wanquan Liu
author: Louis Caccetta
author: Yong Wang
author: Xin Zhang
published in: Journal of Optimization Theory and Applications
publication date: 2016-10-20T00:00:00Z
review text: The subject of the article is located in a scientifically active area of finding a sparse solution for linear equations. It usually includes a formulation into a combinatorial optimization problem which is usually relaxed as a convex or a non-convex problem. The authors investigate the non-convex problem with the nonnegative constraint which has an application in signal reconstruction. They consider obtaining Lipschitz continuous problem from the non-Lipschitz one to reduce the computational complexity of the original problem and develop a fast algorithm based on the limited-memory BFGS algorithm to find its sparse solution. They show that the proposed algorithm has better or comparable performance in terms of the CPU time by producing more sparse solutions than convex methods or non-convex methods. This article is well written, structured and explained, it contains five sections: Section 1 Introduction, Section 2 Preliminaries, Section 3 A reformulation, Section 4 Algorithm description, and Section 5 Numerical illustrations, and Section 6 Conclusion. In fact, future scientific work on other application fields such as face recognition and image signal decomposition as well as investigating the equivalence relationship would be interesting.
reviewed by: Başak Akteke-Öztürk
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C27
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 6641402
zbMATH Keywords: nonnegative sparse solution
zbMATH Keywords: non-Lipschitz continuous
zbMATH Keywords: non-convex optimization problem
zbMATH Keywords: combinatorial optimization
zbMATH Keywords: signal reconstruction
zbMATH Keywords: computational complexity
zbMATH Keywords: algorithm
zbMATH Keywords: limited-memory BFGS algorithm
describes a project that uses: l1_ls
describes a project that uses: L-BFGS
describes a project that uses: LBFGS-B
MaRDI profile type: Publication
full work available at URL: s10957-016-0869-2
OpenAlex ID: W2308325646
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DOI: 10.1007/S10957-016-0869-2
description: scientific article; zbMATH DE number 6641402