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.
Original languageEnglish
Pages (from-to)421-430
Number of pages10
JournalJournal of Optimization Theory and Applications
Volume187
DOIs
Publication statusPublished - 2020

Keywords

  • Convex set
  • Extension
  • Normed linear space
  • Quasiconvex function

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