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Bot, Radu Ioan; Hodrea, Ioan Bogdan; Wanka , Gert : ε -optimality conditions for composed convex optimization problems

Bot, Radu Ioan ; Hodrea, Ioan Bogdan ; Wanka , Gert : ε -optimality conditions for composed convex optimization problems

Author(s):
Bot, Radu Ioan
Hodrea, Ioan Bogdan
Wanka , Gert
Title:
ε -optimality conditions for composed convex optimization problems
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 15, 2007
Mathematics Subject Classification:
90C46 [ Optimality conditions, duality ]
49N15 [ Duality theory ]
90C25 [ Convex programming ]
Abstract:
The aim of the present paper is to provide a formula for the ε - subdifferential of f + g o h different from the ones which can be found in the existent literature. Further we equivalently characterize this formula by using of a so-called closedness type regularity condition expressed by means of the epigraphs of the conjugates of the functions involved. Even more, using the ε - subdifferential formula we are able to derive necessary and sufficient conditions for the ε - optimal solutions of composed convex optimization problems.
Keywords:
conjugate functions, composed convex functions, ε - subdifferential, ε - optimality conditions
Language:
English
Publication time:
9 / 2007