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Constraint qualifications for optimality conditions and total Lagrange dualities in convex infinite programming. (English) Zbl 1218.90200
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:
90C34Semi-infinite programming
90C25Convex programming
52A07Convex sets in topological vector spaces (convex geometry)
41A29Approximation with constraints
90C46Optimality conditions, duality