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

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED Optimization Letters 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

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.