An implementation of Newton-like methods on nonlinearly constrained networks

The minimization of a nonlinear function with linear and nonlinear constraints and simple bounds can be performed by minimizing an augmented Lagrangian function, including only the nonlinear constraints. This procedure is particularly interesting when the linear constraints are flow conservation equations, as there exist efficient techniques for solving nonlinear network problems. It is then necessary to estimate their multipliers, and variable reduction techniques can be used to carry out the successive minimizations. This work analyzes the possibility of estimating the multipliers of the nonlinear constraints using Newton-like methods. Also, an algorithm is designed to solve nonlinear network problems with nonlinear inequality side constraints, which combines first and superlinear-order multiplier methods. The computational performance of this method is compared with that of MINOS 5.5.