scholarly journals Towards Supremum-Sum Subdifferential Calculus Free of Qualification Conditions

2016 ◽  
Vol 26 (4) ◽  
pp. 2219-2234 ◽  
Author(s):  
R. Correa ◽  
A. Hantoute ◽  
M. A. López
Keyword(s):  
Subdifferential Calculus ◽  
Qualification Conditions

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

1999 ◽  
Vol 40 (3) ◽  
pp. 353-378 ◽  
Author(s):  
C. Zặlinescu
Keyword(s):  
Convex Programming ◽  
Constraint Qualification ◽  
Constraint Qualifications ◽  
Strong Duality ◽  
Sufficient Condition ◽  
Subdifferential Calculus ◽  
Infinite Dimensional ◽  
Qualification Conditions ◽  
The One

In 1990 Gowda and Teboulle published the paper [16], making a comparison of several conditions ensuring the Fenchel-Rockafellar duality formulainf{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].

On Metric and Calmness Qualification Conditions in Subdifferential Calculus

2008 ◽  
Vol 16 (2-3) ◽  
pp. 199-227 ◽  
Author(s):  
Alexander D. Ioffe ◽  
Jiří V. Outrata
Keyword(s):  
Subdifferential Calculus ◽  
Qualification Conditions

Subdifferential calculus without qualification conditions, using approximate subdifferentials: A survey

1995 ◽  
Vol 24 (12) ◽  
pp. 1727-1754 ◽  
Author(s):  
J.-B. Hiriart-Urruty ◽  
M. Moussaoui ◽  
A. Seeger ◽  
M. Volle
Keyword(s):  
Subdifferential Calculus ◽  
Qualification Conditions
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