Constraint Qualifications for Inexact Linear Programs
Jean‐Charles Pomerol · 1979
The duality theorem of [6] states: If the value of (P) is finite, then there exists (y74)ER+mXC such that yA-wi=O and is equal to the value of (P1). This result does not hold without constraint qualification. Actually, the result ([4] Th. 28.2.2) invoked by Soyster [6] implies the existence of a Kuhn-Tucker vector only if there exists a feasible x belonging to ri(dom fo), which is here different from R'n (fo denoting the objective function to minimize, i.e., fo(x)=supcec ). We will first construct two examples that show that the duality theorem above fails without constraint qualification. Then we shall give a new condition that ensures that this theorem holds. This condition is a general constraint qualification available in convex programming [3] and is