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