Efficient dual methods for nonlinearly constrained networks

Abstract

The minimization of nonlinearly constrained network flow problems can be performed by exploiting the efficiency of the network flow techniques. It lies in minimizing approximately a series of (augmented) Lagrangian functions including only the side constraints, subject to balance constraints in the nodes and capacity bounds. One of the drawbacks of the multiplier methods with quadratic penalty function when is applied to problems with inequality constraints is that the corresponding augmented Lagrangian function is not twice continuously differentiable even if the cost and constraint functions are. The author's purpose is to put forward two methods that overcome this difficulty: the exponential multiplier method and the ε-subgradient method, and to compare their efficiency with that of the quadratic multiplier method and that of the codes MINOS and LOQO. The results are encouraging. © Springer-Verlag Berlin Heidelberg 2005.