On the Extension of Continuous Quasiconvex Functions

Carlo Alberto Bernardi ()
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Carlo Alberto Bernardi: Università Cattolica del Sacro Cuore

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 2, No 7, 430 pages

Abstract: Abstract We study the problem of extending continuous quasiconvex real-valued functions from a subspace of a real normed linear space. Our results are essentially finite-dimensional and are based on a technical lemma which permits to “extend” a nested family of open convex subsets of a given subspace to a nested family of open convex sets in the whole space, in such a way that certain topological conditions are satisfied.

Keywords: Quasiconvex function; Extension; Convex set; Normed linear space; Primary 52A41; Secondary 26B25; 46A99 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01767-x

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