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Fakultät für Mathematik
Bot, Radu Ioan; Csetnek, Ernö Robert; Wanka, Gert : Regularity conditions via quasi-relative interior in convex programming

Bot, Radu Ioan ; Csetnek, Ernö Robert ; Wanka, Gert : Regularity conditions via quasi-relative interior in convex programming


Author(s):
Bot, Radu Ioan
Csetnek, Ernö Robert
Wanka, Gert
Title:
Regularity conditions via quasi-relative interior in convex programming
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 8, 2007
Mathematics Subject Classification:
90C25 [ Convex programming ]
46A20 [ Duality theory ]
90C51 [ Interior-point methods ]
Abstract:
We give some new regularity conditions for Fenchel duality in separated locally convex vector spaces, written in terms of the notion of quasi interior and quasi-relative interior, respectively. We provide also an example of a convex optimization problem for which the classical generalized interior-point conditions given so far in the literature cannot be applied, while the one given by us is applicable. Using a technique developed by Magnanti, we derive some duality results for the optimization problem with cone inequality constraints and its Lagrange dual problem and we show that a duality result recently given in the literature for this pair of problems is incorrect.
Keywords:
convex programming, Fenchel duality, Lagrange duality, quasi-relative interior
Language:
English
Publication time:
3 / 2007

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