{"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/drsom-a-dimension-reduced-second-order-method","title":"DRSOM: A Dimension Reduced Second-Order Method","arxiv_id":"2208.00208","date":"2022-07-30","proceeding":null,"authors":["Chuwen Zhang","Dongdong Ge","Chang He","Bo Jiang","Yuntian Jiang","Yinyu Ye"],"abstract":"In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while using only curvature information in a few directions. Consequently, the computational overhead of our method remains comparable to the first-order such as the gradient descent method. Theoretically, we show that the method has a local quadratic convergence and a global convergence rate of $O(\\epsilon^{-3/2})$ to satisfy the first-order and second-order conditions if the subspace satisfies a commonly adopted approximated Hessian assumption. We further show that this assumption can be removed if we perform a corrector step using a Krylov-like method periodically at the end stage of the algorithm. The applicability and performance of DRSOM are exhibited by various computational experiments, including $L_2 - L_p$ minimization, CUTEst problems, and sensor network localization.","url_abs":"https://arxiv.org/abs/2208.00208v3","url_pdf":"https://arxiv.org/pdf/2208.00208v3.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":"drsom-a-dimension-reduced-second-order-method","repo_url":"https://github.com/brentian/DRSOM.jl","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"drsom-a-dimension-reduced-second-order-method","repo_url":"https://github.com/COPT-Public/DRSOM.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"drsom-a-dimension-reduced-second-order-method","repo_url":"https://github.com/bzhangcw/drsom.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"sgd","method_name":"SGD"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2208.00208","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}