Pathfollowing methods in nonlinear optimization III: Lagrange multiplier embedding

Pathfollowing methods in nonlinear optimization III: Lagrange multiplier embedding

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Article ID: iaor19961814
Country: Germany
Volume: 41
Issue: 2
Start Page Number: 127
End Page Number: 152
Publication Date: Mar 1995
Journal: Mathematical Methods of Operations Research (Heidelberg)
Authors: , , ,
Keywords: lagrange multipliers
Abstract:

This paper deals with Lagrange multiplier methods which are interpreted as pathfollowing methods. The author investigates 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 the authors 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 the present research with respect to penalty methods (part I) and exact penalty methods (part II).

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