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

Electronic source:

application/pdf

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