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arXiv · 1603.04782

On the Kantorovich's theorem for Newton's method for solving generalized equations under the majorant condition

Gilson N. Silva
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Abstract

In this paper we consider a version of the Kantorovich's theorem for solving the generalized equation $F(x)+T(x)\ni 0$, where $F$ is a Fr\'echet derivative function and $T$ is a set-valued and maximal monotone acting between Hilbert spaces. We show that this method is quadratically convergent to a solution of $F(x)+T(x)\ni 0$. We have used the idea of majorant function, which relaxes the Lipschitz continuity of the derivative $F'$. It allows us to obtain the optimal convergence radius, uniqueness of solution and also to solving generalized equations under Smale's condition.

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Gilson N. Silva. 2016-03-15. On the Kantorovich's theorem for Newton's method for solving generalized equations under the majorant condition. https://arxiv.org/abs/1603.04782

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