ODE versus SQP methods for constrained optimization

In this paper, we review some methods which are designed to solve equality constrained minimization problems by following the trajectory defined by a system of ordinary differential equations. The numerical performance of a number of these methods is compared with that of some popular sequential quadratic programming algorithms. On a set of eighteen difficult test problems, we observe that several of the ODE methods are more successful than any of the SQP techniques. We suggest that these experimental results indicate the need for research both to analyze and develop new ODE techniques and also to strengthen the currently available SQP algorithms.This work was supported by a SERC Research Studentship for the first author. Both authors are indebted to Dr. J. J. McKeown and Dr. K. D. Patel of SCICON Ltd., the collaborating establishment, for their advice and encouragement.