Journal of Convex Analysis 16 (2009), No. 3, 845--856
Copyright Heldermann Verlag 2009
Qualification-Free Optimality Conditions for Convex Programs with Separable Inequality Constraints
Guo Yin Li
Dept. of Applied Mathematics, University of New South Wales, Sydney 2052, Australia
g.li@unsw.edu.au
Vaithilingam Jeyakumar
Dept. of Applied Mathematics, University of New South Wales, Sydney 2052, Australia
v.jeyakumar@unsw.edu.au
We show that separable convex functions enjoy ε-subdifferential sum formula as well as the Fenchel duality without a regularity assumption, and establish that for convex programs with separable convex constraints a new partially asymptotic Lagrange multiplier conditions hold without a constraint qualification. Examples are given to illustrate the results.
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