Nonconvex and Nonsmooth Sparse Optimization via Adaptively Iterative Reweighted Methods
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.
Cite
@article{arxiv.1810.10167,
title = {Nonconvex and Nonsmooth Sparse Optimization via Adaptively Iterative Reweighted Methods},
author = {Hao Wang and Fan Zhang and Yuanming Shi and Yaohua Hu},
journal= {arXiv preprint arXiv:1810.10167},
year = {2021}
}