Work

Variable Smoothing Alternating Proximal Gradient Algorithm for Coupled Composite Optimization

Year: 2026

Type: article

Abstract: In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques with first-order methods, we propose a variable smoothing alternating proximal gradient algorithm that features flexible parameter choices for step sizes and smoothing levels. Under mild assumptions, we establish that the iteration complexity to reach an $$\varepsilon $$ ε -approximate stationary point is $$\mathcal {O}(\varepsilon ^{-3})$$ O ( ε - 3 ) . The proposed algorithm is evaluated on sparse signal recovery and image denoising problems. Numerical experiments demonstrate its effectiveness and superiority over existing algorithms.

Source: Journal of Optimization Theory and Applications

DOI: 10.1007/s10957-026-02966-8

Authors: Xian-Jun Long, Kang Zeng, Gao-Xi Li, Minh N. Dao, Zai-Yun Peng

Institutions: Chongqing Technology and Business University, RMIT University, Yunnan Normal University

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Science Foundation, National Natural Science Foundation of China, Chongqing Technology and Business University, Australian Research Council