Complete characterization of optimality for convex programming in banach spaces

Conditions for optimality which are both necessary and sufficient are given for convex programming in Banach spaces. They are derived under a rather weak geometrical assumption on the existence of a relative radial point in the feasible set. This assumption is superfluous in finite dimensions. Applications include a duality theorem without a constraint qualification, and a necessary and sufficient version of Pontryagin's principle for optimal control of a convex system.

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