Abstract
This paper addresses the globalization of the semi-smooth Newton method for non-smooth equations F(x) = 0 in \({\mathbb{R}}^m\) with applications to complementarity and discretized ℓ1-regularization problems. Assuming semi-smoothness it is shown that super-linearly convergent Newton methods can be globalized, if appropriate descent directions are used for the merit function |F(x)|2. Special attention is paid to directions obtained from the primal-dual active set strategy.
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K. Ito’s research was partially supported by the Army Research Office under DAAD19-02-1-039.
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Ito, K., Kunisch, K. On a semi-smooth Newton method and its globalization. Math. Program. 118, 347–370 (2009). https://doi.org/10.1007/s10107-007-0196-3
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DOI: https://doi.org/10.1007/s10107-007-0196-3