通过广义微分求 PDE 参数控制问题的稳定性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-05-03 DOI:10.1007/s11228-024-00716-4

N. T. Qui, P.-D. Le Thi

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引用次数: 0

摘要

本文研究了具有有限多个状态约束的半线性椭圆最优控制问题的数学程序设计表述，这使得参数数学程序设计中的结果得以使用。通过应用参数数学程序设计的最新稳定性结果，我们将获得参数控制问题的微分稳定性和倾斜稳定性的一些新结果。一方面，我们推导出了基本参数扰动下控制问题边际函数正则次微分的显式上估计值。另一方面，我们建立了倾斜参数扰动下控制问题的倾斜稳定性特征。

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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Stability for Parametric Control Problems of PDEs via Generalized Differentiation

This paper investigates the mathematical programming formulation of semilinear elliptic optimal control problems with finitely many state constraints, this allows the use of results in parametric mathematical programming. By applying recent stability results in parametric mathematical programming, we will obtain some new results on differential stability and tilt stability for parametric control problems. On the one hand, we derive an explicit upper estimate for regular subdifferential of marginal function of control problems under basic parameter perturbations. On the other hand, we establish a characterization of tilt stability of control problems under tilt parameter perturbations.

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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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