# On a semismooth* Newton method for solving generalized equations

arXiv: https://arxiv.org/abs/1904.09167 · HTML: https://mlsanity.com/paper/1904.09167/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2019.

## Built on by (most cited first, 1 of 1)

- [Active manifolds, stratifications, and convergence to local minima in nonsmooth optimization](https://mlsanity.com/paper/2108.11832/) (2021)

## Abstract (arXiv)

In the paper, a Newton-type method for the solution of generalized equations (GEs) is derived, where the linearization concerns both the single-valued and the multi-valued part of the considered GE. The method is based on the new notion of semismoothness^* which, together with a suitable regularity condition, ensure the local superlinear convergence. An implementable version of the new method is derived for a class of GEs, frequently arising in optimization and equilibrium models.