Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/68643
Title: Existence of augmented lagrange multipliers for semi-infinite programming problems
Authors: Burachik, RS
Yang, XQ 
Zhou, YY
Keywords: Semi-infinite programming
Augmented Lagrange multiplier
Optimality conditions
Sharp Lagrangian
A valley at 0 augmenting function
Issue Date: 2017
Publisher: Springer
Source: Journal of optimization theory and applications, 2017, v. 173, no. 2, p. 471-503 How to cite?
Journal: Journal of optimization theory and applications 
Abstract: Using an augmented Lagrangian approach, we study the existence of augmented Lagrange multipliers of a semi-infinite programming problem and discuss their characterizations in terms of saddle points. In the case of a sharp Lagrangian, we obtain a first-order necessary condition for the existence of an augmented Lagrange multiplier for the semi-infinite programming problem and some first-order sufficient conditions by assuming inf-compactness of the data functions and the extended Mangasarian-Fromovitz constraint qualification. Using a valley at 0 augmenting function and assuming suitable second-order sufficient conditions, we obtain the existence of an augmented Lagrange multiplier for the semi-infinite programming problem.
URI: http://hdl.handle.net/10397/68643
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1007/s10957-017-1091-6
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