{"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/global-optimization-with-a-power-transformed","title":"Global Optimization with A Power-Transformed Objective and Gaussian Smoothing","arxiv_id":"2412.05204","date":"2024-12-06","proceeding":null,"authors":["Chen Xu"],"abstract":"We propose a novel method that solves global optimization problems in two steps: (1) perform a (exponential) power-$N$ transformation to the not-necessarily differentiable objective function $f$ and get $f_N$, and (2) optimize the Gaussian-smoothed $f_N$ with stochastic approximations. Under mild conditions on $f$, for any $\\delta>0$, we prove that with a sufficiently large power $N_\\delta$, this method converges to a solution in the $\\delta$-neighborhood of $f$'s global optimum point. The convergence rate is $O(d^2\\sigma^4\\varepsilon^{-2})$, which is faster than both the standard and single-loop homotopy methods if $\\sigma$ is pre-selected to be in $(0,1)$. In most of the experiments performed, our method produces better solutions than other algorithms that also apply smoothing techniques.","url_abs":"https://arxiv.org/abs/2412.05204v2","url_pdf":"https://arxiv.org/pdf/2412.05204v2.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":"global-optimization-with-a-power-transformed","repo_url":"https://github.com/chen-research/GS-PowerTransform","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[{"task_slug":"global-optimization","task_name":"global-optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}