Sparse recovery by the iteratively reweighted algorithm for elastic minimization. (3rd October 2017)

• Record Type: Journal Article
• Authors: Zhang, Yong; Ye, WanZhou
• Is Part Of: Optimization. Volume 66:Number 10(2017)
• Page Start: 1677
• Page End: 1687
• Publication Date: 2017-10-03
• Subjects: Elastic minimization -- nonconvex optimization -- stationary point -- convergence; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1359590
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, we propose an iteratively reweighted minimization algorithm (IRL1 algorithm) for solving the elastic minimization problem. We prove that any sequence generated by the IRL1 algorithm is bounded and asymptotically regular. We also prove that the sequence is convergent for any rational and the limit is a stationary point of the elastic minimization problem. Moreover, under certain conditions, we present an error bound between the limit point of convergent sequence and the sparse solution of underdetermined linear system . Numerical experiments on sparse vector recovery are presented to demonstrate the effectiveness of the proposed algorithm.