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<p>We propose and analyze asymptotic proximal point (APP) methods to find a global minimizer under a mild assumption. The method is based on an asymptotic representation of nonconvex proximal points so that it can find the global minimizer without being trapped in saddle points, local minima, or even discontinuities. Our results show that this method enjoys global linear convergence with high probability for all functions satisfying the assumption. Numerical experiments and comparisons in various dimensions from 2 to 500 demonstrate the benefits of the method.</p>

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Asymptotic Proximal Point Methods for Global Optimization

  • 期刊论文

  • 发表日期：

    2025年11月16日

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  • Xiaopeng Luo,
  • Xin Xu,
  • Herschel Rabitz

摘要

We propose and analyze asymptotic proximal point (APP) methods to find a global minimizer under a mild assumption. The method is based on an asymptotic representation of nonconvex proximal points so that it can find the global minimizer without being trapped in saddle points, local minima, or even discontinuities. Our results show that this method enjoys global linear convergence with high probability for all functions satisfying the assumption. Numerical experiments and comparisons in various dimensions from 2 to 500 demonstrate the benefits of the method.