Kuhn–Tucker Conditions for a Convex Programming Problem in Banach Spaces Partially Ordered by Cone with Empty Interior

Abstract

The existence of saddle point of the Lagrange function for a convex programming problem in Banach spaces ordered by a cone with empty interior is established under a strong simultaneity condition. As a consequence, the Kuhn-Tucker conditions are derived. It is shown that the Slater and the strong simultaneity condition are equivalent if the cone determining the partial order has an interior.