On the First-Order Estimation of Multipliers from Kuhn-Tucker Systems in Multiplier Methods Using Variable Reduction

Abstract

The minimization of a nonlinear function with linear and nonlinear constraints and simple bounds can be performed by minimizing an Augmented Lagrangian function that includes only the nonlinear constraints subject to the linear constraints and simple bounds. It is then necessary to estimate the multipliers of the nonlinear constraints, and variable reduction techniques can be used to carry out the successive minimizations. This procedure is particularly interesting in case of that the linear constraints are flow conservation equations, as there exist efficient techniques to solve nonlinear network problems. In this work the possibility of estimating those multipliers through the Kuhn-Tucker optimality conditions is analyzed and compared with the Hestenes-Powell multiplier estimation. A method is put forward to identify when the first procedure can be safely used indicating an efficient way to compute these estimations. Computational tests are included.