Stability of Minima in Constrained Optimization Problems and Implicit Function Theorem

被引：0
|
作者：
Arutyunov, Aram V. [1 ]
Tsarkov, Kirill A. [1 ]
Zhukovskiy, Sergey E. [1 ,2 ]
机构：
[1] Russian Acad Sci, V A Trapeznikov Inst Control Sci, Moscow, Russia
[2] Moscow Inst Phys & Technol, Dolgoprudnyi, Moscow, Russia
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2024年 / 203卷 / 02期
关键词：
Stability of solutions; Constrained optimization; Parameterized extremal problem; Implicit function theorem;
D O I：
10.1007/s10957-024-02459-6
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
In the paper, we consider both finite-dimensional and infinite-dimensional optimization problems with inclusion-type and equality-type constraints. We obtain sufficient conditions for the stability in the weak topology of a solution to this problem with respect to small perturbations of the problem parameters. In the finite-dimensional case, conditions for the stability in the strong topology of the solution are obtained for the problem with equality-type constraints. These conditions are based on a certain implicit function theorem.
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页码：1293 / 1308
页数：16
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