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Line search filter methods for nonlinear programming: motivation and global convergence. (English) Zbl 1114.90128
Summary: Line search methods are proposed for nonlinear programming using Fletcher and Leyffer’s filter method [R. Flechter and S. Leyffer, Math. Program. 91, No. 2 (A), 239–269 (2002; Zbl 1049.90088)], which replaces the traditional merit function. Their global convergence properties are analyzed. The presented framework is applied to active set sequential quadratic programming (SQP) and barrier interior point algorithms. Under mild assumptions it is shown that every limit point of the sequence of iterates generated by the algorithm is feasible, and that there exists at least one limit point that is a stationary point for the problem under consideration. A new alternative filter approach employing the Lagrangian function instead of the objective function with identical global convergence properties is briefly discussed.

90C30Nonlinear programming
49M37Methods of nonlinear programming type in calculus of variations
65K05Mathematical programming (numerical methods)
90C51Interior-point methods
90C55Methods of successive quadratic programming type
ipfilter; Ipopt