A Robust Implementation of a
Sequential Quadratic Programming Algorithm with Successive Error Restoration
K. Schittkowski, Optimization Letters, Vol. 5, 283-296 (2011)
Abstract:
We consider sequential quadratic programming (SQP) methods for solving
constrained nonlinear programming problems. It is generally believed that SQP
methods are sensitive to the accuracy by which partial derivatives are provided.
One reason is that differences of gradients of the Lagrangian function are used
for updating a quasi-Newton matrix, e.g., by the BFGS formula. The purpose of
this paper is to show by numerical experimentation that the method can be
stabilized substantially. Even in case of large random errors leading to partial
derivatives with at most one correct digit, termination subject to an accuracy
of 10-7 can be achieved, at least in 90 % of 306 problems of a
standard test suite. The algorithm is stabilized by a non-monotone line search
and, in addition, by internal and external restarts in case of errors when
computing the search direction due to inaccurate derivatives. Additional
safeguards are implemented to overcome the situation that an intermediate
feasible iterate might get an objective function value smaller than the final
stationary point. In addition, we show how initial and periodic scaled restarts
improve the efficiency in a situation with very slow convergence.
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