Related papers: Fast convergence to higher multiplicity zeros
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
In recent years, accelerated extra-gradient methods have attracted much attention by researchers, for solving monotone inclusion problems. A limitation of most current accelerated extra-gradient methods lies in their direct utilization of…
This paper studies a finite element discretization of the regularized Bingham equations that describe viscoplastic flow. An efficient nonlinear solver for the discrete model is then proposed and analyzed. The solver is based on Anderson…
In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov's accelerating approach, our methods rely on a so-called…
A new method of root finding is formulated that uses a numerical iterative process involving three points. A given function y = f(x) whose roots are desired is fitted and approximated by a polynomial function of the form P(x)= a(x-b)^N that…
In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method…
Empirical results show that Anderson acceleration (AA) can be a powerful mechanism to improve the asymptotic linear convergence speed of the Alternating Direction Method of Multipliers (ADMM) when ADMM by itself converges linearly. However,…
The present author recently proposed and proved a relationship theorem between nonlinear polynomial equations and the corresponding Jacobian matrix. By using this theorem, this paper derives a Newton iterative formula without requiring the…
A method is given for finding roots of a one-variable function using Taylor's expansion of that function and fractional derivative calculated at a suitable tangent point without using Newton's method, but is regarded as a variant of Halley…
Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative…
Anderson Acceleration (AA) is a method to accelerate the convergence of fixed point iterations for nonlinear, algebraic systems of equations. Due to the requirement of solving a least squares problem at each iteration and a reliance on…
We propose, analyze, and test a nonlinear preconditioning technique to improve the Newton iteration for non-isothermal flow simulations. We prove that by first applying an Anderson accelerated Picard step, Newton becomes unconditionally…
The paper presents (human-oriented) specification and (pen-and-paper) verification of the square root function. The function implements Newton method and uses a look-up table for initial approximations. Specification is done in terms of…
This paper introduces a simple variant of the power method. It is shown analytically and numerically to accelerate convergence to the dominant eigenvalue/eigenvector pair; and, it is particularly effective for problems featuring a small…
In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…
We consider the solution of variational equations on manifolds by Newton's method. These problems can be expressed as root finding problems for mappings from infinite dimensional manifolds into dual vector bundles. We derive the…
We introduce a new iterative root-finding method for complex polynomials, dubbed {\it Newton-Ellipsoid} method. It is inspired by the Ellipsoid method, a classical method in optimization, and a property of Newton's Method derived in…
Newton's method for polynomial root finding is one of mathematics' most well-known algorithms. The method also has its shortcomings: it is undefined at critical points, it could exhibit chaotic behavior and is only guaranteed to converge…
In this paper we study the convergence of Newton-Raphson method. For this method there exists some convergence results which are practically not very useful and just guarantee the convergence of this method when the first term of this…
Unconstrained convex optimization problems have enormous applications in various field of science and engineering. Different iterative methods are available in literature to solve such problem, and Newton method is among the oldest and…