Existence of Augmented Lagrange Multipliers for Semi-infinite Programming Problems |
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Authors: | R S Burachik X Q Yang Y Y Zhou |
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Institution: | 1.School of Information Technology and Mathematical Sciences,University of South Australia,Adelaide,Australia;2.Department of Applied Mathematics,The Hong Kong Polytechnic University,Hong Kong,China;3.Department of Mathematics,Soochow University,Suzhou,China |
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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. |
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