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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). 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.

Global Convergence of a Hybrid Trust-Region SQP-Filter Algorithm for General Nonlinear Programming