Are weaker stationarity concepts of stochastic MPCC problems significant in absence of SMPCC-LICQ?

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-05-10 DOI:10.1007/s11590-024-02115-y

Arnab Sur

引用次数: 0

Abstract

In this article, we study weak stationarity conditions (A- and C-) for a particular class of degenerate stochastic mathematical programming problems with complementarity constraints (SMPCC, for short). Importance of the weak stationarity concepts in absence of SMPCC-LICQ are presented through toy problems in which the point of local or global minimizers are weak stationary points rather than satisfying other stronger stationarity conditions. Finally, a well known technique to solve stochastic programming problems, namely sample average approximation (SAA) method, is studied to show the significance of the weak stationarity conditions for degenerate SMPCC problems. Consistency of weak stationary estimators are established under weaker constraint qualifications than SMPCC-LICQ.

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在没有 SMPCC-LICQ 的情况下，随机 MPCC 问题的较弱静止性概念是否重要？

在本文中，我们研究了一类特殊的带互补约束的退化随机数学程序设计问题（简称 SMPCC）的弱静止条件（A- 和 C-）。通过局部或全局最小化点为弱静止点而非满足其他更强静止条件的玩具问题，介绍了弱静止概念在无 SMPCC-LICQ 时的重要性。最后，研究了一种众所周知的解决随机程序设计问题的技术，即样本平均逼近（SAA）方法，以说明弱静止条件对于退化 SMPCC 问题的重要性。在比 SMPCC-LICQ 更弱的约束条件下，建立了弱静态估计器的一致性。

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.

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