Methods for Nonlinear Constraints in Optimization Calculations

     Andrew R. Conn  Nicholas I. M. Gould    Philippe L. Toint

                        Report 96/6


Ten years ago, the broad consensus among researchers in constrained
optimization   was  that  sequential  quadratic  programming  (SQP)
methods  were the  methods of choice. While, in the long term, this
position may be justified, the past ten years have exposed a number
of  difficulties  with  the  SQP  approach.  Moreover,  alternative
methods  have  shown  themselves  capable  of  solving  large-scale
problems.   In this  paper,  we shall outline the  defects with SQP
methods,  and  discuss the alternatives.  In particular,  we  shall
indicate  how our understanding of the subproblems which inevitably
arise  in  constrained optimization calculations  has  improved. We
shall  also  consider the  impact  of  interior-point  methods  for
inequality  constrained  problems,   described  elsewhere  in  this
volume, and  argue  that these methods likely provide a more useful
Newton model for  such problems  than do traditional  SQP  methods.
Finally, we shall  consider trust-region  methods  for  constrained
problems, and  the impact of automatic differentiation on algorithm
design.