Related papers: An Adaptive Newton-Method Based on a Dynamical Sys…
The renormalization method based on the Taylor expansion for asymptotic analysis of differential equations is generalized to difference equations. The proposed renormalization method is based on the Newton-Maclaurin expansion. Several basic…
In this paper we develop an adaptive procedure for the numerical solution of semilinear parabolic problems, with possible singular perturbations. Our approach combines a linearization technique using Newton's method with an adaptive…
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…
This paper details a novel indirect method for solving constrained optimal control problems (OCPs) directly in continuous-time function space. The KKT conditions are embedded in a non-smooth complementarity function, which enables their…
This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable…
We introduce a new dynamical system, at the interface between second-order dynamics with inertia and Newton's method. This system extends the class of inertial Newton-like dynamics by featuring a time-dependent parameter in front of the…
We present a principled approach for designing stochastic Newton methods for solving finite sum optimization problems. Our approach has two steps. First, we re-write the stationarity conditions as a system of nonlinear equations that…
In stochastic optimization, a common tool to deal sequentially with large sample is to consider the well-known stochastic gradient algorithm. Nevertheless, since the stepsequence is the same for each direction, this can lead to bad results…
A nonlinear operator equation $F(x)=0$, $F:H\to H,$ in a Hilbert space is considered. Continuous Newton's-type procedures based on a construction of a dynamical system with the trajectory starting at some initial point $x_0$ and becoming…
The Newton's method for solving stationary Navier-Stokes equations (NSE) is known to convergent fast, however, may fail due to a bad initial guess. This work presents a simple-to-implement nonlinear preconditioning of Newton's iteration,…
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…
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…
Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses local Quasi-Newton…
Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume…
Adaptive cubic regularization methods for solving nonconvex problems need the efficient computation of the trial step, involving the minimization of a cubic model. We propose a new approach in which this model is minimized in a low…
Motivated by machine learning problems over large data sets and distributed optimization over networks, we develop and analyze a new method called incremental Newton method for minimizing the sum of a large number of strongly convex…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
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…
This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…
In design of optical systems based on LED (Light emitting diode) technology, a crucial task is to handle the unstructured data describing properties of optical elements in standard formats. This leads to the problem of data fitting within…