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In this paper, we propose a new method that combines the inexact Newtonmethod with a procedure to obtain a feasible inexact projection for solvingconstrained smooth and nonsmooth equations. The local convergence theorems areestablished under the assumption of smoothness or semismoothness of thefunction that defines the equation and its regularity at the solution. Inparticular, we show that a sequence generated by the method converges to asolution with linear, superlinear, or quadratic rate, under suitableconditions. Moreover, some numerical experiments are reported to illustrate thepractical behavior of the proposed method.

Inexact Newton method with feasible inexact projections for solving constrained smooth and nonsmooth equations