Dinkelbach Type Approximation Algorithms for Nonlinear Fractional Optimization Problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-05 DOI:10.1080/01630563.2023.2217893

A. Orzan, R. Precup

引用次数: 1

Abstract

Abstract In this paper we establish some approximation versions of the classical Dinkelbach algorithm for nonlinear fractional optimization problems in Banach spaces. We start by examining what occurs if at any step of the algorithm, the generated point desired to be a minimizer can only be determined with a given error. Next we assume that the step error tends to zero as the algorithm advances. The last version of the algorithm we present is making use of Ekeland’s variational principle for generating the sequence of minimizer-like points. In the final part of the article we deliver some results in order to achieve a Palais-Smale type compactness condition that guarantees the convergence of our Dinkelbach-Ekeland algorithm.

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非线性分式优化问题的Dinkelbach型逼近算法

摘要本文建立了Banach空间中非线性分式优化问题的经典Dinkelbach算法的一些近似版本。我们首先检查如果在算法的任何一步，生成的希望成为最小值的点只能在给定误差的情况下确定，会发生什么。接下来，我们假设随着算法的发展，步长误差趋于零。我们提出的算法的最后一个版本是利用Ekeland的变分原理生成类极小点序列。在文章的最后部分，我们给出了一些结果，以实现Palais-Smale型紧性条件，该条件保证了我们的Dinkelbach-Ekeland算法的收敛性。

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.