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.

引用

页码：1293 / 1308

页数：16

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