In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however applied in different underlying Hilbert spaces. Most importantly, the algorithms allow to process the bounded linear operators and the set-valued operators occur...

In his classic book, Modern Algebra, van der Waerden gave a procedure for factoring polynomials over a …nite-dimensional, separable, simple extension …eld. I believe that there is a nonconstructive component to his proof, and I will indicate where it comes in and why. Although I’m sure that this component could be avoided while staying within the framework that he set down, it is simpler to get...

A problem is presented about the evolutionary process of the vertex splitting complex network. The rule of the evolution is: every newly-added vertex is the copy of or is split from the existing vertex. The analytic equation set of this network evolutionary model and arithmetic of iteration are put forward. A series of simulation calculation prove that the complex network is Scale Free Network ...

Controlled system islanding, also called system splitting, can effectively prevent blackouts of power systems. The splitting strategy determining how to split a power network into islands should be given in real time. Previous papers proposed an ordered binary decision diagrammethod to search for the splitting strategies satisfying necessary steady-state constraints, e.g. generation– load balan...

We consider the problem of splitting an order for R goods, R ≥ 1, among a set of sellers, each having bounded amounts of the goods, so as to minimize the total cost of the deal. In deal splitting with packages (DSP), the sellers offer packages containing combinations of the goods; in deal splitting with price tables (DST), the buyer can generate such combinations using price tables. Our problem...

System splitting problem, also known as controlled system separation problem, is to determine the proper splitting points for splitting the entire power network into islands when island operation of system is unavoidable. By “proper” we mean that the splitting strategies should guarantee both the power balance and satisfaction to capacity constraints of transmission lines and other facilities i...