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Partially finite convex programming. I: Quasi relative interiors and duality theory. (English) Zbl 0778.90049

Summary: 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.
[For part II see the authors, ibid. 57B, No. 1, 49-83 (1992; Zbl 0778.90050)].

MSC:

90C25 Convex programming
90C34 Semi-infinite programming
90C48 Programming in abstract spaces
49N15 Duality theory (optimization)

Citations:

Zbl 0778.90050
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References:

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