... need the notion of the affine hull of a convexsetX[denotedaff(X)]. This is the intersection of all hyperplanes containingX.• The relative interior of X, denotedri(X), is the set of allx ... Fur-thermore, the optimal valuef∗is finite and thereexists a vector¯x ∈ Xsuch thatgj(¯x) < 0, ∀ j =1, ,r.•Strong Duality Theorem: There exists at leastone geometric multiplier and there ... Xs.t. there exists>0withz |z − x <, z∈ aff(X)⊂ X,that is,ri(X)is the interior of Xrelative toaff(X).•Every nonempty convex set has a nonemptyrelative interior.DUALITY THEOREM...