A comparison of constraint qualifications in infinite-dimensional convex programming revisited
Constantin Zălinescu · ANZIAM Journal · 1999
In 1990 Gowda and Teboulle published the paper [16], making a comparison of several conditions ensuring the Fenchel-Rockafellar duality formula inf{ f ( x ) + g ( Ax ) | x ∈ X } = max{− f *( A * y *) − g *(− y *) | y * ∈ Y *}. Probably the first comparison of different constraint qualification conditions was made by Hiriart-Urruty [17] in connection with ε-subdifferential calculus. Among them appears, as the basic sufficient condition, the formula for the conjugate of the corresponding function; such functions are: f 1 + f 2 , g o A , max{ f l ,…, f n }, etc. In fact strong duality formulae (like the one above) and good formulae for conjugates are equivalent and they can be used to obtain formulae for ε-subdifferentials, using a technique developed in [17] and extensively used in [46].