An Inertial‐Relaxed Newton‐Type Projection Method for Solving Nonlinear Equations With Applications

ABSTRACT In this paper, based on the famous inexact Newton method and the inertial‐relaxed technique, we propose an inertial‐relaxed Newton‐type projection method for solving nonlinear equations. The global convergence of the proposed method is established without the Lipschitz continuity and pseudo‐monotonicity of the underlying mapping. Moreover, under the local Lipschitz continuity, we show the iteration‐complexity bound for finding an ‐approximation solution with being a given precision. To the best of our knowledge, this is the first iteration‐complexity result associated with Newton‐type projection methods in the literature under such an assumption. Preliminary numerical experiments on standard nonlinear equations show that the proposed method is competitive and promising. Applying the proposed method to solving Tikhonov‐regularized logistic regression problems verifies the efficiency and robustness of the proposed method.