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A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces
Author(s) -
Boţ Radu Ioan,
Grad SorinMihai,
Wanka Gert
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510662
Subject(s) - subderivative , mathematics , convex conjugate , duality (order theory) , constraint (computer aided design) , convex analysis , convex set , regular polygon , pure mathematics , function (biology) , pseudoconvex function , convex function , proper convex function , mathematical analysis , convex optimization , geometry , evolutionary biology , biology
In this paper we work in separated locally convex spaces where we give equivalent statements for the formulae of the conjugate function of the sum of a convex lower‐semicontinuous function and the precomposition of another convex lower‐semicontinuous function which is also K ‐increasing with a K ‐convex K ‐epi‐closed function, where K is a nonempty closed convex cone. These statements prove to be the weakest constraint qualifications given so far under which the formulae for the subdifferential of the mentioned sum of functions are valid. Then we deliver constraint qualifications inspired from them that guarantee some conjugate duality assertions. Two interesting special cases taken from the literature conclude the paper. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)