Geodesic
A new regular multiplier embedding
Kybernetika, Tome 49 (2013) no. 2, pp. 236-257 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Embedding approaches can be used for solving non linear programs P. The idea is to define a one-parametric problem such that for some value of the parameter the corresponding problem is equivalent to P. A particular case is the multipliers embedding, where the solutions of the corresponding parametric problem can be interpreted as the points computed by the multipliers method on P. However, in the known cases, either path-following methods can not be applied or the necessary conditions for its convergence are fulfilled under very restrictive hypothesis. In this paper, we present a new multipliers embedding such that the objective function and the constraints of $P(t)$ are $C^3$ differentiable functions. We prove that the parametric problem satisfies the JJT-regularity generically, a necessary condition for the success of the path-following method.
Embedding approaches can be used for solving non linear programs P. The idea is to define a one-parametric problem such that for some value of the parameter the corresponding problem is equivalent to P. A particular case is the multipliers embedding, where the solutions of the corresponding parametric problem can be interpreted as the points computed by the multipliers method on P. However, in the known cases, either path-following methods can not be applied or the necessary conditions for its convergence are fulfilled under very restrictive hypothesis. In this paper, we present a new multipliers embedding such that the objective function and the constraints of $P(t)$ are $C^3$ differentiable functions. We prove that the parametric problem satisfies the JJT-regularity generically, a necessary condition for the success of the path-following method.
Classification : 49M30, 90C31
Keywords: Jongen–Jonker–Twilt regularity; multipliers method; embedding 
@article{KYB_2013_49_2_a3,
     author = {Bouza Allende, Gemayqzel and Guddat, J\"urgen},
     title = {A new regular multiplier embedding},
     journal = {Kybernetika},
     pages = {236--257},
     year = {2013},
     volume = {49},
     number = {2},
     mrnumber = {3085395},
     zbl = {1266.90178},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013_49_2_a3/}
}
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Bouza Allende, Gemayqzel; Guddat, Jürgen. A new regular multiplier embedding. Kybernetika, Tome 49 (2013) no. 2, pp. 236-257. http://geodesic.mathdoc.fr/item/KYB_2013_49_2_a3/