Nonconvex and Nonsmooth Sparse Optimization via Adaptively Iterative Reweighted Methods

Hao Wang (), Fan Zhang, Yuanming Shi and Yaohua Hu
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Hao Wang: ShanghaiTech University
Fan Zhang: ShanghaiTech University
Yuanming Shi: ShanghaiTech University
Yaohua Hu: Shenzhen University

Journal of Global Optimization, 2021, vol. 81, issue 3, No 7, 717-748

Abstract: Abstract We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a wide range of applications. We design a general algorithmic framework of iteratively reweighted algorithms for solving the proposed nonconvex and nonsmooth sparse optimization problems, which solves a sequence of weighted convex regularization problems with adaptively updated weights. First-order optimality condition is derived and global convergence results are provided under loose assumptions, making our theoretical results a practical tool for analyzing a family of various reweighted algorithms. The effectiveness and efficiency of our proposed formulation and the algorithms are demonstrated in numerical experiments on various sparse optimization problems.

Keywords: Nonconvex and nonsmooth sparse optimization; Iteratively reweighted methods (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10898-021-01093-0

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