Nonconvex and Nonsmooth Sparse Optimization via Adaptively Iterative Reweighted Methods

Hao Wang; Fan Zhang; Yuanming Shi; Yaohua Hu

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arXiv · 1810.10167

Nonconvex and Nonsmooth Sparse Optimization via Adaptively Iterative Reweighted Methods

Hao Wang·Fan Zhang·Yuanming Shi·Yaohua Hu

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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.

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BibTeX RIS

Hao Wang, Fan Zhang, Yuanming Shi, Yaohua Hu. 2018-10-24. Nonconvex and Nonsmooth Sparse Optimization via Adaptively Iterative Reweighted Methods. https://arxiv.org/abs/1810.10167

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