Remarks on general infinite dimensional duality with cone and equality constraints. (English) Zbl 1209.90289
Summary: We prove a strong duality result between a convex optimization problem with both cone and equality constraints and its Lagrange dual formulation, provided that a constraint qualification condition related to the notion of quasi-relative interior holds true. In such a way we overcome the difficulty that the interior of the set involved in the regularity condition is empty.
MSC:
90C25 | Convex programming |
90C46 | Optimality conditions and duality in mathematical programming |
46A22 | Theorems of Hahn-Banach type; extension and lifting of functionals and operators |
49N15 | Duality theory (optimization) |