Related papers: Inexact Newton's method to nonlinear functions wit…
We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…
In this paper, using generalized metric projection, we propose a new extragradient method for finding a common element of the solutions set of a generalized equilibrium problem and a variational inequality for an $\alpha$-inverse-strongly…
Newton's method is the most widespread high-order method, demanding the gradient and the Hessian of the objective function. However, one of the main disadvantages of Newtons method is its lack of global convergence and high iteration cost.…
In this paper, we investigate global convergence properties of the inexact nonsmooth Newton method for solving the system of absolute value equations (AVE). Global $Q$-linear convergence is established under suitable assumptions. Moreover,…
Let $E$ be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone and satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired…
In this paper we study Newton's method for solving generalized equations in Banach spaces. We show that under strong regularity of the generalized equation, the method is locally convergent to a solution with superlinear/quadratic rate. The…
We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possible nonsmooth DC function. The application of proximal DC algorithms to address this problem…
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features an adaptive choice of the damping parameter in the Newton…
This paper deals with the minimization of large sum of convex functions by Inexact Newton (IN) methods employing subsampled functions, gradients and Hessian approximations. The Conjugate Gradient method is used to compute the inexact Newton…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
We study Newton type methods for inverse problems described by nonlinear operator equations $F(u)=g$ in Banach spaces where the Newton equations $F'(u_n;u_{n+1}-u_n) = g-F(u_n)$ are regularized variationally using a general data misfit…
We study a class of monotone inclusions called "self-concordant inclusion" which covers three fundamental convex optimization formulations as special cases. We develop a new generalized Newton-type framework to solve this inclusion. Our…
This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to…
Let $\left( X,\left\Vert \cdot\right\Vert_{X}\right) $ and $\left( Y,\left\Vert \cdot\right\Vert_{Y}\right) $ be Banach spaces over $\mathbb{R},$ with $X$ uniformly convex and compactly embedded into $Y.$ The inverse iteration method is…
Interior-point methods for linear programming problems require the repeated solution of a linear system of equations. Solving these linear systems is non-trivial due to the severe ill-conditioning of the matrices towards convergence. This…
This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
We consider Tikhonov-type variational regularization of ill-posed linear operator equations in Banach spaces with general convex penalty functionals. Upper bounds for certain error measures expressing the distance between exact and…
The $m$-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified provided that the operator…
In this short work we consider nonlinear equation in Banach space $x = A(x)$. We combine classical Newton method with Vietoris method to propose new more general method. Under rather general conditions about the noise we investigate local…