In this paper, we suggest and analyze an improved generalized Newton method for solving the NP-hard absolute value equations [Formula: see text] when the singular values of A exceed 1. We show that the global and local quadratic convergence of the proposed method. Numerical experiments show the efficiency of the method and the high accuracy of calculation.

Many problems in image processing are addressed via the minimization of a cost functional. The most prominent optimization technique is the gradient descent, often used due to its simplicity and applicability where other techniques, e.g., those coming from discrete optimization, can not be used. Yet, gradient descent suffers from a slow convergence, and often to just local minima which highly d...

In this paper, we study the existence and uniqueness theorem for solving the generalized operator equation of the form F(x) + G(x) + T(x) ∋ 0, where F is a Fréchet differentiable operator, G is a maximal monotone operator and T is a Lipschitzian operator defined on an open convex subset of a Hilbert space. Our results are improvements upon corresponding results of Uko [Generalized equations and...

We present new semilocal convergence theorems for Newton methods in a Banach space. Using earlier general conditions we find more precise error estimates on the distances involved using the majorant principle. Moreover we provide a better information on the location of the solution. In the special case of Newton’s method under Lipschitz conditions we show that the famous Newton–Kantorovich hypo...

The preconditioned generalized shift-splitting (PGSS) iteration method is unconditionally convergent for solving saddle point problems with nonsymmetric coefficient matrices. By making use of the PGSS as inner solver Newton method, we establish a class Newton-PGSS large sparse nonlinear system Jacobian matrices about problems. For new presented give local convergence analysis and semilocal unde...

A class of Lagrange-Newton-SQP methods is investigated for optimal control problems governed by semilinear parabolic initial-boundary value problems. Distributed and boundary controls are given, restricted by pointwise upper and lower bounds. The convergence of the method is discussed in appropriate Banach spaces. Based on a weak second order suucient optimality condition for the reference solu...

We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we call generalized self-concordant functions. This notion allows us to develop a unified framework for designing Newton-type methods to solve convex optimization problems. The prop...

In this paper, we aim to explore properties of a class of NCP-functions and investigate a related semismooth Newton method for complementarity problems. Some favorite properties about the class of NCP-functions and its merit function are discussed including strong semismoothness, continuous differentiability and the nonsingularity of the element in C-subdifferential. In particular, we present a...