How Mature is Nonlinear Optimization?

                     Nick Gould and Philippe L. Toint

                             Report 03/04

Numerical  methods  for  solving  nonlinear optimization  problems  have  been
developed for over  50 years.  Has this field reached  maturity?  What are the
current research  frontiers and ongoing  challenges? These are  questions that
this paper attempts  to clarify, if not fully answer.  The discussion does not
explore the  technical intricacies  of nonlinear optimization  techniques, but
instead focusses on concepts and research practice. The field's vibrant nature
is illustrated by  a number of applications, such as  adaptive lens design for
spectacles,  the piloting  of injection  of dangerous  drugs to  patients, the
identification  of   parameters  in   biochemical  models  of   neurons,  food
sterilization or animation techniques for video games.