On the efficiency of multiplier methods for nonlinear network problems with nonlinear constraints

Abstract

The minimization of network flow problems with linear/nonlinear side constraints can be performed by minimizing an augmented Lagrangian function, including only the side constraints. This method gives rise to an algorithm that combines first‐ and superlinear‐order estimators of the multipliers of the side constraints. The code PFNRN03 is the implementation of this algorithm in Fortran 77. The main aim of this work is to compare the efficiency of this code on two sets of (industrial, artificial) test problems with that of the general‐purpose solvers MINOS, SNOPT, LANCELOT and LOQO. Numerical results of these four codes are obtained by the NEOS server with AMPL input. The comparison indicates that PFNRN03 may be effective on current large‐scale network flow problems with nonlinear side constraints.