相关论文: New versions of Newton method: step-size choice, c…

We will consider the damped Newton method for strongly monotone and Lipschitz continuous operator equations in a variational setting. We will provide a very accessible justification why the undamped Newton method performs better than its…

An iterative formula based on Newton Method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root. In addition, the method…

We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiability, which generalizes semi-smoothness. The classic notion…

We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…

The Newton method is a powerful optimization algorithm, valued for its rapid local convergence and elegant geometric properties. However, its theoretical guarantees are usually limited to convex problems. In this work, we ask whether…

Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical…

Newton's method is a fundamental technique in optimization with quadratic convergence within a neighborhood around the optimum. However reaching this neighborhood is often slow and dominates the computational costs. We exploit two…

In this paper, we propose and analyze some practical Newton methods for electronic structure calculations. We show the convergence and the local quadratic convergence rate for the Newton method when the Newton search directions are…

Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for simple strongly convex problems, no straightforward variant…

A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…

We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…

Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…

This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…

In this paper, an idea to solve nonlinear equations is presented. During the solution of any problem with Newton's Method, it might happen that some of the unknowns satisfy the convergence criteria where the others fail. The convergence…

In this paper, we consider the problem of solving a constrained system of nonlinear equations. We propose an algorithm based on a combination of the Newton and conditional gradient methods, and establish its local convergence analysis. Our…

We first investigate properties of M-tensor equations. In particular, we show that if the constant term of the equation is nonnegative, then finding a nonnegative solution of the equation can be done by finding a positive solution of a…

We propose two variants of Newton method for solving unconstrained minimization problem. Our method leverages optimization techniques such as penalty and augmented Lagrangian method to generate novel variants of the Newton method namely the…

It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a…

We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods…