通过广义微分求 PDE 参数控制问题的稳定性

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Set-Valued and Variational Analysis 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

Set-Valued and Variational Analysis MATHEMATICS, APPLIED-

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The scope of the journal includes variational analysis and its applications to mathematics, economics, and engineering; set-valued analysis and generalized differential calculus; numerical and computational aspects of set-valued and variational analysis; variational and set-valued techniques in the presence of uncertainty; equilibrium problems; variational principles and calculus of variations; optimal control; viability theory; variational inequalities and variational convergence; fixed points of set-valued mappings; differential, integral, and operator inclusions; methods of variational and set-valued analysis in models of mechanics, systems control, economics, computer vision, finance, and applied sciences. High quality papers dealing with any other theoretical aspect of control and optimization are also considered for publication.