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Partially finite convex programming, part I: quasi relative interiors and duality theory

Borwein, Jonathan M. and Lewis, Adrian (1992) Partially finite convex programming, part I: quasi relative interiors and duality theory. Mathematical Programming, 57 (1). pp. 15-48.

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Abstract

We study convex programs that involve the minimization of a convex function over a convex subset of a topological vector space, subject to a finite number of linear inequalities. We develop the notion of the quasi relative interior of a convex set, an extension of the relative interior in finite dimensions. We use this idea in a constraint qualification for a fundamental Fenchel duality result, and then deduce duality results for these problems despite the almost invariable failure of the standard Slater condition. Part II of this work studies applications to more concrete models, whose dual problems are often finite-dimensional and computationally tractable.

Item Type: Article
Subjects: UNSPECIFIED
Faculty: UNSPECIFIED
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 18 Feb 2015 14:31
Last Modified: 18 Feb 2015 14:31
URI: https://docserver.carma.newcastle.edu.au/id/eprint/1571

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