On functions whose stationary points are global minima

I. Zang, E. U. Choo, M. Avriel

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, a characterization of functions whose stationary points are global minima is studied. By considering the level sets of a real function as a point-to-set mapping, and by examining its semicontinuity properties, we obtain the result that a real function, defined on a subset of Rn and satisfying some mild regularity conditions, belongs to the above family iff the point-to-set mapping of its level sets is strictly lower semicontinuous. Mathematical programming applications are also mentioned.

Original languageEnglish
Pages (from-to)195-208
Number of pages14
JournalJournal of Optimization Theory and Applications
Volume22
Issue number2
DOIs
StatePublished - Jun 1977

Keywords

  • Stationary point
  • global minima
  • optimality conditions
  • point-to-set mapping

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