Models for the piecewise linear unsplittable multicommodity flow problems

The Method for Solving a Piecewise-Linear Multicommodity Flow Problem

The paper deals with a flow distribution problem with a piecewise-linear cost function. The problem is formulated as a piecewise-linear programming problem which is not separable with respect to separate variable group. The method for solving this problem is based on the extension of the idea of the simplex method to the class of non-separable piecewise-linear problems. It secures finding of a ...

Reformulations by Discretization for Piecewise Linear Integer Multicommodity Network Flow Problems

Interior Point Methods for Linear Multicommodity Flow Problems

This article studies the linear multicommodity network flow problem. This kind of problem arises in a wide variety of contexts. A numerical implementation of the primal-dual interior-point method is designed to solve the problem. In the interior-point method, at each iteration, the corresponding linear problem, expressed as an augmented indefinite system, is solved by using the AINV algorithm c...

Improved Approximation Algorithms for Unsplittable Flow Problems

In the single-source unsplittable ow problem we are given a graph G; a source vertex s and a set of sinks t 1 ; : : :; t k with associated demands. We seek a single s-t i ow path for each commodity i so that the demands are satissed and the total ow routed across any edge e is bounded by its capacity c e : The problem is an NP-hard variant of max ow and a generalization of single-source edge-di...

Multicommodity Network Flow Problems

In this paper, we consider to apply a primal-dual proximal point algorithm to the multicommodity network flow problem. A remarkable feature of the algorithm consists in how to find an approximate saddle point of the augmented Lagrangian of the problem. In particular, at each iteration, an approximate solution of the subproblem always satisfies the flow conservation equations for all commodities...