Lagrange Multipliers in Locally Convex Spaces

被引：0

作者：

Bachir, Mohammed ^{[1
]}

Blot, Joel ^{[1
]}

机构：

[1] Univ Paris 1 Pantheon Sorbonne, Lab SAMM 4543, Paris, France

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2024年 / 201卷 / 03期

关键词：

Lagrange multipliers; Optimization problems; Admissible sets; Equi-Gateaux-differentiability; APPROXIMATE SUBDIFFERENTIALS; REGULARITY; EXISTENCE;

D O I：

10.1007/s10957-024-02428-z

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：

We give a general Lagrange multiplier rule for mathematical programming problems in a Hausdorff locally convex space. We consider infinitely many inequality and equality constraints. Our results gives in particular a generalisation of the result of Jahn (Introduction to the theory of nonlinear optimization, Springer, Berlin, 2007), replacing Frechet-differentiability assumptions on the functions by the Gateaux-differentiability. Moreover, the closed convex cone with a nonempty interior in the constraints is replaced by a strictly general class of closed subsets introduced in the paper and called "admissible sets". Examples illustrating our results are given.

引用

页码：1275 / 1300

页数：26

共 50 条

[21] On stratifiable locally convex spaces
Shkarin, SA
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 1999, 6 (04) : 435 - 460
[22] SUMMABILITY IN LOCALLY CONVEX SPACES
BOEL, J
DUHOUX, M
ANNALES DE LA SOCIETE SCIENTIFIQUE DE BRUXELLES SERIES 1-SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1972, 86 (01): : 12 - &
[23] LOCALLY CONVEX SYNTOPOGENOUS SPACES
BURGESS, DCJ
FITZPATRICK, M
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1979, 85 (MAY) : 445 - 448
[24] On measures in locally convex spaces
Uglanov, AV
HIGH DIMENSIONAL PROBABILITY III, 2003, 55 : 43 - 54
[25] CONVEX COMPACTNESS PROPERTY IN LOCALLY CONVEX SPACES
OSTLING, EG
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (03): : A371 - A371
[26] SEQUENCES IN LOCALLY CONVEX SPACES
HAMPSON, JK
WILANSKY, A
STUDIA MATHEMATICA, 1973, 45 (03) : 221 - 223
[27] THE APPROXIMATION ON LOCALLY CONVEX SPACES
Song Wenhua Dalian University of Technology
Approximation Theory and its Applications, 1994, (01) : 26 - 33
[28] PROJECTIONS IN LOCALLY CONVEX SPACES
LOHMAN, RH
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (05): : A646 - &
[29] Operators on Locally Convex Spaces
Zelazko, Wieslaw
RECENT ADVANCES IN OPERATOR THEORY AND APPLICATIONS, 2009, 187 : 237 - 247
[30] ORTHOCOMPLEMENTATIONS AND LOCALLY CONVEX SPACES
WILBUR, WJ
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (07): : A761 - A762

← 1 2 3 4 5 →