Two-step and three-step Q-superlinear convergence of SQP methods

This paper investigates the convergence rates of the variable-multiplier pair (x, ) in sequential quadratic programming methods for equality constrained optimization. The two main results of the paper are that the Q-superlinear convergence of {x_k} implies two-step Q-superlinear convergence for {(x_k, _k)} and that the two-step Q-superlinear convergence of {x_k} implies three-step Q-superlinear convergence for {(x_k, _k)}.The author is indebted to Professor Richard Tapia for many helpful comments and suggestions on the paper. The comments by Professors A. R. Conn and N. I. M. Gould on an earlier version are also acknowledged. This research was funded by SERC and ESRC research contracts.