{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/linear-convergence-of-proximal-gradient","title":"Linear Convergence of Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems","arxiv_id":"1512.09302","date":"2015-12-31","proceeding":null,"authors":["Bo Wen","Xiaojun Chen","Ting Kei Pong"],"abstract":"In this paper, we study the proximal gradient algorithm with extrapolation\nfor minimizing the sum of a Lipschitz differentiable function and a proper\nclosed convex function. Under the error bound condition used in [19] for\nanalyzing the convergence of the proximal gradient algorithm, we show that\nthere exists a threshold such that if the extrapolation coefficients are chosen\nbelow this threshold, then the sequence generated converges $R$-linearly to a\nstationary point of the problem. Moreover, the corresponding sequence of\nobjective values is also $R$-linearly convergent. In addition, the threshold\nreduces to $1$ for convex problems and, as a consequence, we obtain the\n$R$-linear convergence of the sequence generated by FISTA with fixed restart.\nFinally, we present some numerical experiments to illustrate our results.","url_abs":"http://arxiv.org/abs/1512.09302v2","url_pdf":"http://arxiv.org/pdf/1512.09302v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"linear-convergence-of-proximal-gradient","repo_url":"https://github.com/EvanZhuang/MRI-Reconstruction-with-Sparse-Optimization","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}