Partially finite convex programming,Part I: Quasi relative interiors and duality theory |
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Authors: | J. M. Borwein A. S. Lewis |
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Affiliation: | (1) Department of Mathematics, Statistics and Computing Science, Dalhousie University, B3H 3J5 Halifax, N.S., Canada;(2) Present address: Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, N2L 3G1 Waterloo, Ont., Canada |
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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. |
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Keywords: | Primary 90C25, 49B27 Secondary 90C48, 52A07, 65K05 |
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