On the efficiency of the ε -subgradient methods over nonlinearly constrained networks

Abstract

The efficiency of the network flow techniques can be exploited in the solution of nonlinearly constrained network flow problems by means of approximate sub-gradient methods. In particular, we consider the case where the side constraints (non-network constraints) are convex. We propose to solve the dual problem by using ε-subgradient methods given that the dual function is estimated by minimizing approximately a Lagrangian function with only network constraints. Such Lagrangian function includes the side constraints. In order to evaluate the efficiency of these ε-subgradient methods some of them have been implemented and their performance computationally compared with that of other well-known codes. The results are encouraging. © 2006 International Federation for Information Processing.