Kuhn-Tucker conditions for a convex programming problem in Banach spaces partially ordered by cone with empty interior

TL;DR

This paper derives Kuhn-Tucker conditions for convex programming in Banach spaces ordered by cones with empty interior, establishing equivalence of Slater and strong simultaneity conditions when the cone has an interior point.

Contribution

It extends Kuhn-Tucker theory to Banach spaces with cones having empty interior and clarifies the relationship between Slater and strong simultaneity conditions.

Findings

Kuhn-Tucker conditions are obtained under strong simultaneity.

Equivalence of Slater and strong simultaneity conditions when the cone has an interior point.

Theoretical extension of convex programming conditions in Banach spaces.

Abstract

Kuhn-Tucker conditions for mathematical programming problems in Banach spaces partially ordered by cone with empty interior are obtained under strong simultaneity condition. If partial ordered cone has interior point, it is proved that Slater and strong simultaneity conditions are equivalent.