Inexact direct-search methods for bilevel optimization problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-21 DOI:10.1007/s10589-024-00567-7

Youssef Diouane, Vyacheslav Kungurtsev, Francesco Rinaldi, Damiano Zeffiro

引用次数: 0

Abstract

In this work, we introduce new direct-search schemes for the solution of bilevel optimization (BO) problems. Our methods rely on a fixed accuracy blackbox oracle for the lower-level problem, and deal both with smooth and potentially nonsmooth true objectives. We thus analyze for the first time in the literature direct-search schemes in these settings, giving convergence guarantees to approximate stationary points, as well as complexity bounds in the smooth case. We also propose the first adaptation of mesh adaptive direct-search schemes for BO. Some preliminary numerical results on a standard set of bilevel optimization problems show the effectiveness of our new approaches.

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双层优化问题的非精确直接搜索方法

在这项工作中，我们为双层优化（BO）问题的求解引入了新的直接搜索方案。我们的方法依赖于下层问题的固定精度黑盒子甲骨文，并同时处理光滑和潜在非光滑真实目标。因此，我们首次在文献中分析了这些情况下的直接搜索方案，给出了近似静止点的收敛保证，以及光滑情况下的复杂度边界。我们还首次提出了适用于 BO 的网格自适应直接搜索方案。对一组标准双层优化问题的初步数值结果表明了我们新方法的有效性。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.