Kybernetika 49 no. 2, 236-257, 2013

A new regular multiplier embedding

Gemayqzel Bouza Allende and Jürgen Guddat


Embedding approaches can be used for solving non linear programs \emph{P}. The idea is to define a one-parametric problem such that for some value of the parameter the corresponding problem is equivalent to \emph{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 \emph{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 \emph{JJT}-regularity generically, a necessary condition for the success of the path-following method.


Jongen-Jonker-Twilt regularity, multipliers method, embedding


90C31, 49M30


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