{"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/derivative-free-global-minimization-for-a","title":"Derivative-free global minimization for a class of multiple minima problems","arxiv_id":"2006.08181","date":"2020-06-15","proceeding":null,"authors":["Xiaopeng Luo","Xin Xu","Daoyi Dong"],"abstract":"We prove that the finite-difference based derivative-free descent (FD-DFD) methods have a capability to find the global minima for a class of multiple minima problems. Our main result shows that, for a class of multiple minima objectives that is extended from strongly convex functions with Lipschitz-continuous gradients, the iterates of FD-DFD converge to the global minimizer $x_*$ with the linear convergence $\\|x_{k+1}-x_*\\|_2^2\\leqslant\\rho^k \\|x_1-x_*\\|_2^2$ for a fixed $0<\\rho<1$ and any initial iteration $x_1\\in\\mathbb{R}^d$ when the parameters are properly selected. Since the per-iteration cost, i.e., the number of function evaluations, is fixed and almost independent of the dimension $d$, the FD-DFD algorithm has a complexity bound $\\mathcal{O}(\\log\\frac{1}{\\epsilon})$ for finding a point $x$ such that the optimality gap $\\|x-x_*\\|_2^2$ is less than $\\epsilon>0$. Numerical experiments in various dimensions from $5$ to $500$ demonstrate the benefits of the FD-DFD method.","url_abs":"http://arxiv.org/abs/2006.08181v2","url_pdf":"http://arxiv.org/pdf/2006.08181v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"derivative-free-global-minimization-for-a","repo_url":"https://github.com/xiaopengluo/dfd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"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}