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A comparison of constraint qualifications in infinite-dimensional convex programming revisited

Published online by Cambridge University Press:  17 February 2009

C. Zặlinescu
C. Zặlinescu
Affiliation:
University “Al. I. Cuza” Iaşi, Faculty of Mathematics, Bd. Copou, Nr. 11, 6600 Iaşi, Romania
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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: f1 + f2, g o A, max{fl,…, fn}, 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].

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 3 , January 1999 , pp. 353 - 378
Copyright
Copyright © Australian Mathematical Society 1999

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