Related papers: An approximate proximal numerical procedure concer…
This article firstly develops a proximal explicit approach for the generalized method of lines. In such a method, the domain of the PDE in question is discretized in lines and the equation solution is written on these lines as functions of…
This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the…
This article provides a general iterative approximation to partial differential equations, and thus establish existence of smooth solution. The heart of the method is to contract (or expand) the boundary conditions uniformly in the domain,…
In this paper, we describe a semi-discrete method for a numerical resolution of a type of partial differential equations, called the method of lines (MOL). This method is based on the discretization of all but one of the variables of the…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embedding method, which uses an implicit representation of the…
We obtain approximate convexity principles for solutions to some classes of nonlinear elliptic partial differential equations in convex domains involving approximately concave nonlinearities. Furthermore, we provide some applications to…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial differential equations. We show the link between the…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
The aim of this paper is to study the characteristics of a general method to produce a new approximation sequence from a given one, by using suitable convex combinations.
This article develops a solution for an inverse problem through the generalized method of lines. We consider a Laplace equation on a domain with internal and external boundaries with standard Dirichlet boundary conditions. Also, we specify…
The derivative expansion approach to the calculation of the interaction between two surfaces, is a generalization of the proximity force approximation, a technique of widespread use in different areas of physics. The derivative expansion…
This paper develops an adaptive generic proximal bundle method, shows its complexity, and presents numerical experiments comparing this method with two bundle methods on a set of optimization problems.
It is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear abstract functional differential equations in both, the finite and infinite delay case. A generalization of the integral…
We propose a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the…
Employing the ideas of non-linear preconditioning and testing of the classical proximal point method, we formalise common arguments in convergence rate and convergence proofs of optimisation methods to the verification of a simple…
For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…