On functions whose local minima are global

I. Zang*, M. Avriel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, necessary and sufficient conditions for a local minimum to be global are derived. The main result is that a real function, defined on a subset of Rn, has the property that every local minimum is global if, and only if, its level sets are lower-semicontinuous point-to-set mappings.

Original languageEnglish
Pages (from-to)183-190
Number of pages8
JournalJournal of Optimization Theory and Applications
Issue number3-4
StatePublished - Aug 1975
Externally publishedYes


  • Global optimality
  • mathematical programming
  • nonconvex programming
  • nonlinear optimization
  • point-to-set maps


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