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We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions. This analysis provides an estimate of the convergence radius and a clear relationship between the majorant function, which relaxes the Lipschitz continuity of the derivative, and the nonlinear operator under consideration. It also allow us to obtain some important special cases
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity operator w
For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate sub-probl
We propose a inexact Newton method for solving inverse eigenvalue problems (IEP). This method is globalized by employing the classical backtracking techniques. A global convergence analysis of this method is provided and the R-order convergence prope
In Wang et al. (J. Optim. Theory Appl., textbf{181}: 216--230, 2019), a class of effective modified Newton-tpye (MN) iteration methods are proposed for solving the generalized absolute value equations (GAVE) and it has been found that the MN iteratio
In the present paper, we consider the semilocal convergence problems of the two-step Newton method for solving nonlinear operator equation in Banach spaces. Under the assumption that the first derivative of the operator satisfies a generalized Lipsch