Global Convergence of a Hybrid Trust-Region SQP-Filter Algorithm for General Nonlinear Programming N.I.M. Gould and Ph. L. Toint Report 01/07 Global convergence to first-order critical points is proved for a variant of the trust-region SQP-filter algorithm analyzed in Fletcher, Gould, Leyffer and Toint (1999). This variant allows the use of two types of step strategies: the first decomposes the step into its normal and tangential components, while the second replaces this decomposition by a stronger condition on the associated model decrease.