On the use of the quasi-relative interior in optimization |
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Authors: | C Z?linescu |
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Institution: | 1. Faculty of Mathematics, University Alexandru Ioan Cuza, Ia?i, Romania.;2. Institute of Mathematics Octav Mayer, Ia?i, Romania.zalinesc@uaic.ro |
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Abstract: | The notion of quasi-relative interior was introduced by Borwein and Lewis in 1992 and applied for duality results in partially finite convex optimization problems. In the last 10 years, several articles were dedicated to duality results in infinite-dimensional scalar, vector and set-valued optimization problems using this notion. The aim of this paper is to refine and discuss such results. We do this observing that the notion of quasi-relative interior is related to (non-proper) separation of a convex set and some of its elements, then pointing out the relation between the subdifferentiability of a function associated to a set of epigraph type at a certain point and the fact that a corresponding point is not in the quasi-relative interior of the closed convex hull of the set. |
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Keywords: | constrained optimization duality Lagrange function quasi-interior quasi-relative interior scalar optimization set-valued optimization subdifferential |
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