A new regular multiplier embedding. (English) Zbl 1266.90178

Summary: 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.


90C31 Sensitivity, stability, parametric optimization
49M30 Other numerical methods in calculus of variations (MSC2010)
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