Existence of Augmented Lagrange Multipliers for Semi-infinite Programming Problems

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 a...

Full description

Saved in:
Bibliographic Details
Published in:Journal of optimization theory and applications 2017-05, Vol.173 (2), p.471-503
Main Authors: Burachik, R. S., Yang, X. Q., Zhou, Y. Y.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied mathematics
Calculus of Variations and Optimal Control
Optimization
Engineering
Lagrange multiplier
Lagrange multipliers
Mathematical analysis
Mathematical functions
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Programming
Saddle points
Semidefinite programming
Studies
Theory of Computation
Valleys
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-017-1091-6