Existence of Augmented Lagrange Multipliers for Semi-infinite Programming Problems

R. S. Burachik (), X. Q. Yang () and Y. Y. Zhou ()
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R. S. Burachik: University of South Australia
X. Q. Yang: The Hong Kong Polytechnic University
Y. Y. Zhou: Soochow University

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 2, No 6, 503 pages

Abstract: 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.

Keywords: Semi-infinite programming; Augmented Lagrange multiplier; Optimality conditions; Sharp Lagrangian; A valley at 0 augmenting function; 90C26; 90C34; 90C46 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-017-1091-6

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