Lagrange Multipliers in Locally Convex Spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-09 DOI:10.1007/s10957-024-02428-z

Mohammed Bachir, Joël Blot

引用次数: 0

Abstract

We give a general Lagrange multiplier rule for mathematical programming problems in a Hausdorff locally convex space. We consider infinitely many inequality and equality constraints. Our results gives in particular a generalisation of the result of Jahn (Introduction to the theory of nonlinear optimization, Springer, Berlin, 2007), replacing Fréchet-differentiability assumptions on the functions by the Gateaux-differentiability. Moreover, the closed convex cone with a nonempty interior in the constraints is replaced by a strictly general class of closed subsets introduced in the paper and called “admissible sets”. Examples illustrating our results are given.

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局部凸空间中的拉格朗日乘数

我们给出了豪斯多夫局部凸空间中数学程序设计问题的一般拉格朗日乘法规则。我们考虑了无限多的不等式和等式约束。我们的结果尤其是对 Jahn（《非线性优化理论导论》，施普林格出版社，柏林，2007 年）的结果的概括，用 Gateaux-differentiability 代替了对函数的 Fréchet-differentiability 假设。此外，约束条件中具有非空内部的封闭凸锥被本文引入的一类严格意义上的封闭子集所取代，该类子集被称为 "可容许集"。本文举例说明了我们的结果。

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.