Regularity Conditions via Quasi-Relative Interior in Convex Programming

Authors:
Radu Ioan Boţ;Ernö Robert Csetnek;Gert Wanka
Affiliations:
radu.bot@mathematik.tu-chemnitz.de and robert.csetnek@mathematik.tu-chemnitz.de and gert.wanka@mathematik.tu-chemnitz.de;-;-
Venue:
SIAM Journal on Optimization
Year:
2008

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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. By using a technique developed by Magnanti, we derive some duality results for the optimization problem with cone constraints and its Lagrange dual problem, and we show that a duality result recently given in the literature for this pair of problems has self-contradictory assumptions.