利用单调算子理论进行三级和多级优化

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Mathematical Methods of Operations Research Pub Date : 2024-02-28 DOI:10.1007/s00186-024-00852-5

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引用次数: 0

摘要

摘要我们考虑了一类多层次优化问题，即在嵌套凸优化问题的最优性约束下，凸目标函数要最小化。作为一个特例，我们考虑了一个三层优化问题，其中下两层的目标由一个光滑项和一个非光滑项的总和组成。基于定点理论和相关论证，我们提出了一种自然一阶算法，并分析了其在若干参数条件下的收敛性和收敛率。

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Trilevel and multilevel optimization using monotone operator theory

Abstract

We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term. Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters.

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来源期刊

Mathematical Methods of Operations Research 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This peer reviewed journal publishes original and high-quality articles on important mathematical and computational aspects of operations research, in particular in the areas of continuous and discrete mathematical optimization, stochastics, and game theory. Theoretically oriented papers are supposed to include explicit motivations of assumptions and results, while application oriented papers need to contain substantial mathematical contributions. Suggestions for algorithms should be accompanied with numerical evidence for their superiority over state-of-the-art methods. Articles must be of interest for a large audience in operations research, written in clear and correct English, and typeset in LaTeX. A special section contains invited tutorial papers on advanced mathematical or computational aspects of operations research, aiming at making such methodologies accessible for a wider audience. All papers are refereed. The emphasis is on originality, quality, and importance.