A primal DPG method without a first-order reformulation

A primal DPG method without a first-order reformulation

We show that it is possible to apply the DPG methodology without reformulating a second order boundary value problem into a first order system, by considering the simple example of the Poisson equation. The result is a new weak formulation and a new DPG method for the Poisson equation, which has no numerical trace variable, but has a numerical flux approximation on the element interfaces, in ad...

A method for solving first order fuzzy differential equation

From first order logic to Nd: a data driven reformulation

First order logic FOL ooers a natural way o f modeling domains such as chemistry: a molecule is most adequately described as a graph of atoms linked by simple or double bonds. To o vercome the speciic diiculties of dealing with FOL, this paper presents an automatic mapping from the initial problem domain onto the set of integer vectors IN d , where d is a user-supplied integer. This mapping ont...

A first-order stochastic primal-dual algorithm with correction step

We investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the stochastic extension to monotone inclusions of a proximal method studied in [26, 35] for saddle point problems. It consists in a forward step determined by the...

A Primal-Dual First-Order Method for Minimization Problems with Linear Constraints

We consider a class of optimization problems with a strongly convex objective function. The feasible set in this class is given as an intersection of a simple convex set with a set given by a number of linear equality and inequality constraints. This class of problems often arises in applications covering the problems of entropylinear programming, ridge regression, elastic net, regularized opti...