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

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Interior Methods for Nonlinear Optimization (2002, background): “In practice many details need to be specified in order to define a convergent filter algorithm; we refer the interested reader to [35, 36].”
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited (2003, methodology): “This nonlinear programming package combines ﬁlter and trust-region methods to globalize an SQP iteration [Fletcher et al. 2002; Fletcher and Leyffer 1998, 2002].”
Retrospective on optimization (2004, methodology): “Termed the filter approach, this method, also developed for trust regions (Fletcher et al., 2001), usually leads to better performance than line searches based on merit functions.”
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming (2006, background): “[13, 15]) we may call a trial step size αk,l for which (19) holds, a “φ-step size.”
Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence (2005, methodology): “[7, 10]), we call αk,l an “f -stepsize,” if it satisfies the f -type switching condition (9), indicating that then decrease of the objective function is required.”