Result: Extensions of the Kuhn--Tucker Constraint Qualification to Generalized Semi-infinite Programming: Extensions of the Kuhn-Tucker constraint qualification to generalized semi-infinite programming

Title:
Extensions of the Kuhn--Tucker Constraint Qualification to Generalized Semi-infinite Programming: Extensions of the Kuhn-Tucker constraint qualification to generalized semi-infinite programming
Authors:
Jan-J. Rückmann, Francisco Guerra Vázquez
Source:
SIAM Journal on Optimization. 15:926-937
Publisher Information:
Society for Industrial & Applied Mathematics (SIAM), 2005.
Publication Year:
2005
Subject Terms:
extended Kuhn-Tucker constraint qualification, Numerical mathematical programming methods, extended Abadie constraint qualification, 0211 other engineering and technologies, generalized semi-infinite programming, 02 engineering and technology, Optimality conditions and duality in mathematical programming, Karush-Kuhn-Tucker theorem, Semi-infinite programming, extended Mangasarian-Fromovitz constraint qualification, local minimizer, Nonconvex programming, global optimization
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1095-7189
1052-6234
DOI:
10.1137/s1052623403431500
Access URL:
https://zbmath.org/2206208
https://doi.org/10.1137/s1052623403431500
Accession Number:
edsair.doi.dedup.....30f9832f4be52bd83c0b79084a52c90c
Database:
OpenAIRE

Further Information

Summary: This paper deals with the class of generalized semi-infinite programming problems (GSIPs) in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be continuously differentiable. We introduce two extensions of the Kuhn-Tucker constraint qualification (which is based on the existence of a tangential continuously differentiable arc) to the class of GSIPs, prove a corresponding Karush-Kuhn-Tucker theorem, and discuss its assumptions. Finally, we present several examples which illustrate for the class of GSIPs some interrelations between the considered extensions of the Mangasarian-Fromovitz constraint qualification, the Abadie constraint qualification, and the Kuhn-Tucker constraint qualification.