On the first-order estimation of multipliers from Kuhn–Tucker systems

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. The viability of estimating the multipliers of the nonlinear constraints from the Kuhn–Tucker system is analyzed and an acceptability test on the residual of the estimation is put forward. The computational performance of the procedure is compared with that of the inexpensive Hestenes–Powell multiplier update.