## Water Finds its Level: A Localized Method for Multicommodity Flow Problem

This paper describes a local-control method for multicommodity flow problem. Both the capacity constraints and the flow conservation constraints are relaxed. If the flow exceeds the capacity on an edge, the edge would have a congestion cost. If the flow into a vertex is not equal to that out of the vertex, the vertex would … Read more

## A multicommodity flow model for rerouting and retiming trains in real-time to reduce reactionary delay in complex station areas

By rerouting and retiming trains in real-time, the propagation of reactionary delay in complex station areas can be reduced. In this study, we propose a new optimisation model and solution algorithm that can be used to determine the best combination of route and schedule changes to make. Whilst several models have been proposed to tackle … Read more

## Distributed Optimization With Local Domain: Applications in MPC and Network Flows

In this paper we consider a network with P nodes, where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector x* minimizing the sum of all the functions. We make the additional assumption that the functions have intersecting local domains, i.e., each function … Read more

## Proximal-ACCPM: a versatile oracle based optimization method

Oracle Based Optimization (OBO) conveniently designates an approach to handle a class of convex optimization problems in which the information pertaining to the function to be minimized and/or to the feasible set takes the form of a linear outer approximation revealed by an oracle. We show, through three representative examples, how difficult problems can be … Read more

## Domination between traffic matrices

A traffic matrix \$D^1\$ dominates a traffic matrix \$D^2\$ if \$D^2\$ can be routed on every (capacitated) network where \$D^1\$ can be routed. We prove that \$D^1\$ dominates \$D^2\$ if and only if \$D^1\$, considered as a capacity vector, supports \$D^2\$. We show several generalizations of this result. Citation Centro Vito Volterra, Universita’ di Roma … Read more