Nonlinear Stepsize Control, Trust Regions and 
              Regularizations for Unconstrained Optimization

                            Ph. L. Toint

             Report 08/15, FUNDP(Namur) 19 october 2008

Abstract.
A general class of algorithms for unconstrained optimization is introduced,
which subsumes the classical trust-region algorithm and two of its newer
variants, as well as the cubic and quadratic regularization methods.  A
unified theory of global convergence to first-order critical points is then
described for this class.