On the Global Convergence of a Filter--SQP Algorithm

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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.”
Mixed Variable Optimization of a Load-Bearing Thermal Insulation System Using a Filter Pattern Search Algorithm (2004, methodology): “Proofs of convergence to a first-order stationary point are given in Fletcher et al. (1998) for SQP and Fletcher et al. (2002) for SLP methods.”
Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming (2002, background): “This approach was generalized by the same authors in [20], where the objective function is approximated by a quadratic model, which results in a sequential quadratic programming (SQP) technique in which each quadratic program must be solved globally.”
Complementarity constraints as nonlinear equations: Theory and numerical experience (2006, methodology): “The filter accepts a trial point whenever the objective or the constraint violation is improved compared with all previous iterates [14, 15, 18].”
Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence (2005, methodology): “Note that the switching conditions used in [6, 9] do not imply this latter relationship.”