The local convergence of an inexact Newton method is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property which is explored as well. Under suitable conditions and without any additional geometric assumptions, local convergence results with linear and quadratic rate and a semi-local convergence result are obtained for the proposed method. Finally, the theory can be applied to problems of finding a singularity of the sum of two vector fields.

翻译：本文研究了求解黎曼流形上广义方程的不精确牛顿法的局部收敛性，并探讨了度量正则性性质。在适当条件下且无需额外几何假设，针对所提方法获得了线性与二次收敛速率的局部收敛结果以及半局部收敛结果。最后，该理论可应用于求解两个向量场之和的奇异性问题。