Constraint Qualification with Schauder Basis for Infinite Programming Problems

被引：0
|
作者：
Bednarczuk, E. M. [1 ]
Lesniewski, K. W. [2 ]
Rutkowski, K. E. [3 ]
机构：
[1] Warsaw Univ Technol, Koszykowa 75, PL-00662 Warsaw, Poland
[2] PAS, Syst Res Inst, Newelska 6, PL-01447 Warsaw, Poland
[3] Cardinal Stefan Wyszynski Univ, Dewajtis 5, PL-01815 Warsaw, Poland
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2023年 / 88卷 / 02期
关键词：
Relaxed constant rank constraint qualification; Abadie constraint qualification; Lagrange multipliers; Rank theorem; Lyusternik-Graves theorem; Schauder basis; Infinite programming problems; Hurwicz set; OPTIMALITY CONDITIONS; EXISTENCE; SYSTEMS; THEOREM; BASES;
D O I：
10.1007/s00245-023-10034-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider infinite programming problems with constraint sets defined by systems of infinite number of inequalities and equations given by continuously differentiable functions defined on Banach spaces. In the approach proposed here we represent these systems with the help of coefficients in a given Schauder basis. We prove Abadie constraint qualification under the new infinite-dimensional Relaxed Constant Rank Constraint Qualification Plus and we discuss the existence of Lagrange multipliers via Hurwicz set. The main tools are: Rank Theorem and Lyusternik-Graves theorem.
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页数：34
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