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On the Extension of Continuous Quasiconvex Functions

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  • Carlo Alberto Bernardi

    (Università Cattolica del Sacro Cuore)

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.

Suggested Citation

  • Carlo Alberto Bernardi, 2020. "On the Extension of Continuous Quasiconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 421-430, November.
    • Handle: RePEc:spr:joptap:v:187:y:2020:i:2:d:10.1007_s10957-020-01767-x
    DOI: 10.1007/s10957-020-01767-x
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    References listed on IDEAS

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    1. Harvey J. Greenberg & William P. Pierskalla, 1971. "A Review of Quasi-Convex Functions," Operations Research, INFORMS, vol. 19(7), pages 1553-1570, December.
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