# Facial reduction for a cone-convex programming problem

Borwein, Jonathan M. and Wolkowicz, H. (1981) Facial reduction for a cone-convex programming problem. Journal Aust. Math. Soc., 30 . pp. 369-380.

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## Abstract

In this paper we study the abstract convex program $\mu = inf{p(x):g(x)\in -S,x\in \Omega}$ (P) where S is an arbitrary convex cone in a finite dimensional space, Q is a convex set and p and g are respectively convex and S-convex (on $\Omega$). We use the concept of a minimal cone for (P) to correct and strengthen a previous characterization of optimality for (P), see Theorem 3.2. The results presented here are used in a sequel to provide a Lagrange multiplier theorem for (P) which holds without any constraint qualification.

Item Type: Article UNSPECIFIED UNSPECIFIED Mrs Naghmana Tehseen 23 Feb 2015 14:02 23 Feb 2015 14:03 https://docserver.carma.newcastle.edu.au/id/eprint/1650