Global Convergence of Trust-Region SQP-Filter 
            Algorithms for General Nonlinear Programming

       Roger Fletcher, Nick Gould, Sven Leyffer and Philippe Toint

                            Report 99/03

Global convergence to first-order critical points is proved for two
trust-region SQP-filter algorithms of the type introduced by Fletcher and
Leyffer (1997). The algorithms allow for an approximate solution of the
quadratic subproblem and incorporate the safeguarding tests described in
Fletcher, Leyffer and Toint (1998). The first algorithm decomposes the step
into its normal and tangential components, while the second replaces this
decomposition by a stronger condition on the associated model decrease.