A non-monotone trust-region algorithm
             for nonlinear optimization 
            subject to convex constraints

                Philippe L. Toint

                  Report 94-24

This paper presents two new trust-region methods for
solving nonlinear optimization  problems over convex
feasible  domains.   These methods are distinguished
by   the  fact  that  they  do  not  enforce  strict
monotonicity of  the  objective function  values  at
successive iterates.  The algorithms  are proved  to
be convergent to critical points of the problem from
any starting point.  Extensive numerical experiments
show that  this  approach  is  competitive with  the
LANCELOT package.