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

Title: Partially finite convex programming, part I: quasi relative interiors and duality theory
Creator: Borwein, J. M.; Lewis, A. S.
Relation: Mathematical Programming Vol. 57, Issue 1-3, p. 15-48
Publisher Link: http://dx.doi.org/10.1007/BF01581072
Publisher: Springer
Resource Type: journal article
Date: 1992
Description: 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.
Subject: convex programming; duality; constraint qualification; Fenchel duality; semi infinite programming
Identifier: http://hdl.handle.net/1959.13/1042509
Identifier: uon:14069
Identifier: ISSN:0025-5610
Language: eng
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