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：本文研究了在Riemann流形上使用度量正则性性质求解广义方程的不精确Newton方法的局部收敛性。在适当条件下且不需要额外的几何假设下，本文得到了这种方法的局部收敛结果，包括线性和二次收敛率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的奇点问题。