Today, practical smooth nonlinear programming problems are routinely solved by sequential quadratic programming (SQP) methods stabilized by a monotone line search procedure subject to a suitable merit function. In case of computational errors as for example caused by inaccurate function or gradient evaluations, however, the approach is unstable and often terminates with an error message. To prevent this situation, a non-monotone line search is proposed which allows the acceptance of a larger steplength. As a by-product, we consider also the possibility to adapt the line search to run under distributed systems. Global convergence of the new SQP algorithm is proved. Numerical results are included, which show that in case of very noisy function values a drastic improvement of the performance is achieved compared to the version with monotone line search.

To download a preprint, click here: nm_sqp2.pdf