TY - JOUR
T1 - Pathfollowing methods in nonlinear optimization III
T2 - Lagrange multiplier embedding
AU - Dentcheva, D.
AU - Guddat, J.
AU - Rückmann, J. J.
AU - Wendler, K.
PY - 1995/6
Y1 - 1995/6
N2 - 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).
AB - 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).
KW - Lagrange multiplier methods
KW - Nonlinear optimization
KW - pathfollowing methods
KW - singularities
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U2 - 10.1007/BF01432651
DO - 10.1007/BF01432651
M3 - Article
AN - SCOPUS:26644456198
SN - 0340-9422
VL - 41
SP - 127
EP - 152
JO - Mathematical Methods of Operations Research
JF - Mathematical Methods of Operations Research
IS - 2
ER -