Related papers: A Globally Convergent Newton Method for Polynomial…

In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…

In recent years, the proximal gradient method and its variants have been generalized to Riemannian manifolds for solving optimization problems with an additively separable structure, i.e., $f + h$, where $f$ is continuously differentiable,…

We consider the problem of numerically identifying roots of a target function - under the constraint that we can only measure the derivatives of the function at a given point, not the function itself. We describe and characterize two…

The reciprocal square root is an important computation for which many sophisticated algorithms exist (see for example \cite{Moroz,863046,863031} and the references therein). A common theme is the use of Newton's method to refine the…

This paper is concerned with an algorithm for finding a singularity of the nonsmooth vector fields. Firstly, we discuss the main results of the Newton method presented in [1] for solving the aforementioned problem. Combining this method…

Many proofs of the fundamental theorem of algebra rely on the fact that the minimum of the modulus of a complex polynomial over the complex plane is attained at some complex number. The proof then follows by arguing the minimum value is…

This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second-order…

In this paper we present GSSN, a globalized SCD semismooth* Newton method for solving nonsmooth nonconvex optimization problems. The global convergence properties of the method are ensured by the proximal gradient method, whereas locally…

In this paper, we introduce an inexact regularized proximal Newton method (IRPNM) that does not require any line search. The method is designed to minimize the sum of a twice continuously differentiable function $f$ and a convex (possibly…

Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a real coefficient polynomial. They can be approximated at a low computational cost if the…

This paper aims to develop a Newton-type method to solve a class of nonconvex composite programs. In particular, the nonsmooth part is possibly nonconvex. To tackle the nonconvexity, we develop a notion of strong prox-regularity which is…

The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…

The LC method described in this work seeks to approximate the roots of polynomial equations in one variable. This book allows you to explore the LC method, which uses geometric structures of Lines L and Circumferences C in the plane of…

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such…

A central computational problem for analyzing and model checking various classes of infinite-state recursive probabilistic systems (including quasi-birth-death processes, multi-type branching processes, stochastic context-free grammars,…

A novel very simple method for finding roots of polynomials over finite fields has been proposed. The essence of the proposed method is to search the roots via nested cycles over the subgroups of the multiplicative group of the Galois…

The DLG root-squaring iterations, due to Dandelin 1826 and rediscovered by Lobachevsky 1834 and Graeffe 1837, have been the main approach to root-finding for a univariate polynomial p(x) in the 19th century and beyond, but not so nowadays…

Policy gradient algorithms have been widely applied to Markov decision processes and reinforcement learning problems in recent years. Regularization with various entropy functions is often used to encourage exploration and improve…

We consider a variant of inexact Newton Method, called Newton-MR, in which the least-squares sub-problems are solved approximately using Minimum Residual method. By construction, Newton-MR can be readily applied for unconstrained…

The Durand-Kerner algorithm is a widely used iterative technique for simultaneously finding all the roots of a polynomial. However, its convergence heavily depends on the choice of initial approximations. This paper introduces two novel…