A New Proximal Iteratively Reweighted Nuclear Norm Method for Nonconvex Nonsmooth Optimization Problems

Zhili Ge, Siyu Zhang, Xin Zhang () and Yan Cui
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Zhili Ge: School of Mathematical Sciences, Nanjing Normal University of Special Education, Nanjing 210038, China
Siyu Zhang: School of Microelectronics and Data Science, Anhui University of Technology, Ma’anshan 243032, China
Xin Zhang: School of Mathematics and Physics, Suqian University, Suqian 223800, China
Yan Cui: School of Artificial Intelligence, Nanjing Normal University of Special Education, Nanjing 210038, China

Mathematics, 2025, vol. 13, issue 16, 1-18

Abstract: This paper proposes a new proximal iteratively reweighted nuclear norm method for a class of nonconvex and nonsmooth optimization problems. The primary contribution of this work is the incorporation of line search technique based on dimensionality reduction and extrapolation. This strategy overcomes parameter constraints by enabling adaptive dynamic adjustment of the extrapolation/proximal parameters ( α k , β k , μ k ). Under the Kurdyka–Łojasiewicz framework for nonconvex and nonsmooth optimization, we prove the global convergence and linear convergence rate of the proposed algorithm. Additionally, through numerical experiments using synthetic and real data in matrix completion problems, we validate the superior performance of the proposed method over well-known methods.

Keywords: nonconvex and nonsmooth optimization; proximal iteratively reweighted method; line search; convergence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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