On Functions Whose Stationary Points Are Global Minima

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 semi-continuity properties, we obtain a result that a real function, defined on a subset of Rn and satisfying some mild regularity conditions, belongs to the above family if and only if the point-to-set mapping of its level sets is strictly lower semicontinuous. Mathematical programming applications are also mentioned.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1976
Accession Number
ADA030691

Entities

People

  • Eng Ung Choo
  • Israel Zang
  • Mordecai Avriel

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • British Columbia
  • Canada
  • Computer Programming
  • Contracts
  • Convex Sets
  • Convolution
  • Intervals
  • Mathematical Programming
  • Numbers
  • Operations Research
  • Real Numbers
  • Sequences
  • Stationary
  • Theorems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.