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).
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This work was supported by the Deutsche Forschungsgemeinschaft under grant Gu 304/1-2.
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Dentcheva, D., Guddat, J., Rückmann, J.J. et al. Pathfollowing methods in nonlinear optimization III: Lagrange multiplier embedding. ZOR - Mathematical Methods of Operations Research 41, 127–152 (1995). https://doi.org/10.1007/BF01432651
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DOI: https://doi.org/10.1007/BF01432651