Line search filter methods for nonlinear programming: motivation and global convergence. (English summary) SIAM J. Optim. 16 (2005), no. 1, 1–31 (electronic). Summary: “Line search methods are proposed for nonlinear programming using R. Fletcher and S. Leyffer’s filter method [Math. Program. 91 (2002), no. 2, Ser. A, 239–269; MR1875517 (2002j:90074)], which replaces the traditional merit function. The global convergence properties of the methods 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.” Reviewed by K. Schittkowsk
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