{"ID":2847426,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.27156","arxiv_id":"2510.27156","title":"Variable Smoothing Alternating Proximal Gradient Algorithm for Coupled Composite Optimization","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 $\\varepsilon$-approximate stationary point is $\\mathcal{O}(\\varepsilon^{-3})$. The proposed algorithm is evaluated on sparse signal recovery and image denoising problems. Numerical experiments demonstrate its effectiveness and superiority over existing algorithms.","short_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 grad...","url_abs":"https://arxiv.org/abs/2510.27156","url_pdf":"https://arxiv.org/pdf/2510.27156v1","authors":"[\"Xian-Jun Long\",\"Kang Zeng\",\"Gao-Xi Li\",\"Minh N. Dao\",\"Zai-Yun Peng\"]","published":"2025-10-31T03:59:10Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}