Asymptotic Proximal Point Methods for Global Optimization

Xiaopeng Luo; Xin Xu; Herschel Rabitz

doi:10.1007/s10915-025-03119-1

Asymptotic Proximal Point Methods for Global Optimization

Xiaopeng Luo
, Xin Xu
, Herschel Rabitz

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Article number	87
Journal	Journal of Scientific Computing
Volume	105
Issue number	3
DOIs	https://doi.org/10.1007/s10915-025-03119-1
State	Published - Dec 2025

All Science Journal Classification (ASJC) codes

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

Keywords

Derivative-free
Global minima
Linear convergence
Multiple minima problem
Nonconvex
Nonsmooth
Proximal point method

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10.1007/s10915-025-03119-1

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title = "Asymptotic Proximal Point Methods for Global Optimization",

abstract = "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.",

keywords = "Derivative-free, Global minima, Linear convergence, Multiple minima problem, Nonconvex, Nonsmooth, Proximal point method",

author = "Xiaopeng Luo and Xin Xu and Herschel Rabitz",

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T1 - Asymptotic Proximal Point Methods for Global Optimization

AU - Luo, Xiaopeng

AU - Xu, Xin

AU - Rabitz, Herschel

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025/12

Y1 - 2025/12

N2 - 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.

AB - 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.

KW - Derivative-free

KW - Global minima

KW - Linear convergence

KW - Multiple minima problem

KW - Nonconvex

KW - Nonsmooth

KW - Proximal point method

UR - https://www.scopus.com/pages/publications/105021980342

UR - https://www.scopus.com/pages/publications/105021980342#tab=citedBy

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DO - 10.1007/s10915-025-03119-1

M3 - Article

AN - SCOPUS:105021980342

SN - 0885-7474

VL - 105

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 3

M1 - 87

ER -

Asymptotic Proximal Point Methods for Global Optimization

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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