Journal of Optimization Theory and Applications

, Volume 48, Issue 1, pp 141–161 | Cite as

One-parameter families of optimization problems: Equality constraints

  • H. Th. Jongen
  • P. Jonker
  • F. Twilt
Contributed Papers

Abstract

In this paper, we introduce generalized critical points and discuss their relationship with other concepts of critical points [resp., stationary points]. Generalized critical points play an important role in parametric optimization. Under generic regularity conditions, we study the set of generalized critical points, in particular, the change of the Morse index. We focus our attention on problems with equality constraints only and provide an indication of how the present theory can be extended to problems with inequality constraints as well.

Key Words

Parametric optimization generalized critical points critical points Morse index quadratic index linear index 

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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • H. Th. Jongen
    • 1
    • 2
  • P. Jonker
    • 1
  • F. Twilt
    • 1
  1. 1.Department of Applied MathematicsTwente University of TechnologyEnschedeThe Netherlands
  2. 2.University of HamburgHamburgGermany

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