Related papers: An adaptive damped Newton method for strongly mono…
In a Hilbert setting, we introduce a new dynamical system and associated algorithms for solving monotone inclusions by rapid methods. Given a maximal monotone operator $A$, the evolution is governed by the time dependent operator $I -(I +…
A local convergence analysis of Newton's method for solving nonlinear equations, under a majorant condition, is presented in this paper. Without assuming convexity of the derivative of the majorant function, which relaxes the Lipschitz…
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,…
Newton's method for finding an unconstrained minimizer for strictly convex functions, generally speaking, does not converge from any starting point. We introduce and study the damped regularized Newton's method (DRNM). It converges globally…
We introduce and prove convergence of a damped Newton algorithm to approximate solutions of the semi-discrete optimal transport problem with storage fees, corresponding to a problem with hard capacity constraints. This is a variant of the…
We investigate a globalized inexact semismooth Newton method applied to strongly convex optimization problems in Hilbert spaces. Here, the semismooth Newton method is appplied to the dual problem, which has a continuously differentiable…
In this paper we continue our work on adaptive timestep control for weakly non- stationary problems. The core of the method is a space-time splitting of adjoint error representations for target functionals due to S\"uli and Hartmann. The…
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…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
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…
We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…
We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions. This analysis provides an estimate of the convergence radius and a clear relationship between the majorant…
The iterative problem of solving nonlinear equations is studied. A new Newton like iterative method with adjustable parameters is designed based on the dynamic system theory. In order to avoid the derivative function in the iterative…
In this paper, we propose a stochastic conformal multi-symplectic method for a class of damped stochastic Hamiltonian partial differential equations in order to inherit the intrinsic properties, and apply the numerical method to solve a…
The nonlinear systems obtained by discretizing degenerate parabolic equations may be hard to solve, especially with Newton's method. In this paper, we apply to Richards equation a strategy that consists in defining a new primary unknown for…
Quasi-Newton methods are widely used for solving convex optimization problems due to their ease of implementation, practical efficiency, and strong local convergence guarantees. However, their global convergence is typically established…
The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…
In this paper, we propose a new method that combines the inexact Newton method with a procedure to obtain a feasible inexact projection for solving constrained smooth and nonsmooth equations. The local convergence theorems are established…
We prove that solution operators of elliptic obstacle-type variational inequalities (or, more generally, locally Lipschitz continuous functions possessing certain pointwise-a.e. convexity properties) are Newton differentiable when…
We derive a posteriori error estimates for the the scalar wave equation discretized in space by continuous finite elements and in time by the explicit leapfrog scheme. Our analysis combines the idea of invoking extra time-regularity for the…