Pathfollowing methods in nonlinear optimization III: Lagrange multiplier embedding

D. Dentcheva, J. Guddat, J. J. Rückmann, K. Wendler

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

This paper deals with Lagrange multiplier methods which are interpreted as pathfollowing methods. We investigate how successful these methods can be for solving "really nonconvex" problems. Singularity theory developed by Jongen-Jonker-Twilt will be used as a successful tool for providing an answer to this question. Certain modifications of the original Lagrange multiplier method extend the possibilities for solving nonlinear optimization problems, but in the worst case we have to find all connected components in the set of all generalized critical points. That is still an open problem. This paper is a continuation of our research with respect to penalty methods (part I) and exact penalty methods (part II).

Original languageEnglish
Pages (from-to)127-152
Number of pages26
JournalMathematical Methods of Operations Research
Volume41
Issue number2
DOIs
StatePublished - Jun 1995

Keywords

  • Lagrange multiplier methods
  • Nonlinear optimization
  • pathfollowing methods
  • singularities

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