A smooth sequential penalty function method for solving nonlinear programming problems

i) The experimental results show that the algorithm converges well and avoids problems due to ill-conditioning of the Hessian of G 22 -1 as r → 0. Values of r<10−30 have been successfully used. ii) It is possible to update G 22 −1 as well as B so that the algorithm does not have to solve any systems of linear equations. Experiment shows that this substantially reduces the cpu time. iii) The Lagrange multipliers are calculated at the solution and decisions as to which constraints to drop (in the inequality constraints case) are then based on the signs and magnitudes of these computed multipliers. This is perhaps the least satisfactory part of the algorithm as the calculation becomes sensitive to rounding errors as the constraints decrease in magnitude.