Multistart algorithm for identifying all optima of nonconvex stochastic functions

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Optimization Letters Pub Date : 2024-05-07 DOI:10.1007/s11590-024-02114-z

Prateek Jaiswal, Jeffrey Larson

引用次数: 0

Abstract

We propose a multistart algorithm to identify all local minima of a constrained, nonconvex stochastic optimization problem. The algorithm uniformly samples points in the domain and then starts a local stochastic optimization run from any point that is the “probabilistically best” point in its neighborhood. Under certain conditions, our algorithm is shown to asymptotically identify all local optima with high probability; this holds even though our algorithm is shown to almost surely start only finitely many local stochastic optimization runs. We demonstrate the performance of an implementation of our algorithm on nonconvex stochastic optimization problems, including identifying optimal variational parameters for the quantum approximate optimization algorithm.

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确定非凸随机函数所有最优值的多开始算法

我们提出了一种多起点算法，用于识别受约束非凸随机优化问题的所有局部最小值。该算法对域中的点进行均匀采样，然后从其邻域中 "概率上最佳 "的任意点开始局部随机优化运行。在某些条件下，我们的算法被证明能以高概率渐近地识别所有局部最优点；即使我们的算法几乎肯定只能启动有限次局部随机优化运行，这一点仍然成立。我们演示了在非凸随机优化问题上实现我们算法的性能，包括确定量子近似优化算法的最优变分参数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.