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Zbl 1218.90200
Fang, D.H.; Li, C.; Ng, K.F.
Constraint qualifications for optimality conditions and total Lagrange dualities in convex infinite programming. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 5, 1143-1159 (2010). ISSN 0362-546X

Summary: For an inequality system defined by an infinite family of proper convex functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications. Under the new constraint qualifications, we provide necessary and/or sufficient conditions for the KKT rules to hold. Similarly, we provide characterizations for constrained minimization problems to have total Lagrangian dualities. Several known results in the conic programming problem are extended and improved.

MSC 2000:: *90C34 Semi-infinite programming
90C25 Convex programming
52A07 Convex sets in topological vector spaces (convex geometry)
41A29 Approximation with constraints
90C46 Optimality conditions, duality

Keywords: convex inequality system; optimality condition; total Lagrangian duality; conic programming

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