Regularizing the abstract convex program

Borwein, Jonathan M. and Wolkowicz, H. (1981) Regularizing the abstract convex program. Journal of Mathematical Analysis and Applications, 83 . pp. 495-530.

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Characterizations of optimality for the abstract convex program (P) where S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set, and p and g are respectively convex and S-convex (on Ω), were given in [10]. These characterizations hold without any constraint qualification. They use the “minimal cone” Sf of (P) and the cone of directions of constancy Dg= (Sf). In the faithfully convex case these cones can be used to regularize (P), i.e., transform (P) into an equivalent program (Pr) for which Slater's condition holds. We present an algorithm that finds both Sf and Dg=(Sf). The main step of the algorithm consists in solving a particular complementarity problem. We also present a characterization of optimality for (P) in terms of the cone of directions of constancy of a convex functional Dφg= rather than Dg=(Sf).

Item Type: Article
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 23 Feb 2015 13:54
Last Modified: 23 Feb 2015 13:54

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