On the superlinear local convergence of a filter-SQP method
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Transition to superlinear local convergence is shown for a modified version of the trust-region filter-SQP method for nonlinear programming introduced by Fletcher, Leyffer, and Toint . Hereby, the original trust-region SQP-steps can be used without an additional second order correction. The main modification consists in using the Lagrangian function value instead of the objective function value in the filter together with an appropriate infeasibility measure. Moreover, it is shown that the modified trust-region filter-SQP method has the same global convergence properties as the original algorithm in .
Key words.nonlinear programming superlinear convergence global convergence filter SQP
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- 1.Bertsekas, D.P.: Constrained optimization and Lagrange multiplier methods. Computer Science and Applied Mathematics, Academic Press Inc., New York, 1982Google Scholar
- 2.Boggs, P.T., Tolle, J.W.: Sequential quadratic programming. In: Acta numerica, Acta Numer., Cambridge Univ. Press, Cambridge, 1995, pp. 1–51Google Scholar
- 3.Chin, C.M, Fletcher, R.: Numerical results for SLPSQP. Filter-SQP and LANCELOT on selected Cute test problems, Tech. Report NA/203, Department of Mathematics, Dundee University, Dundee, Scotland, 2001Google Scholar
- 4.Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-region methods. MPS/SIAM Series on Optimization, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000Google Scholar
- 10.Gonzaga, C.C., Karas, E., Vanti, M.: A globally convergent filter method for nonlinear programming. Technical Report, Department of Mathematics, Federal University of Santa Catarina, Brazil, 2001 (Revised 2002)Google Scholar
- 12.Nocedal, J., Wright, S.J.: Numerical optimization. Springer Series in Operations Research, Springer-Verlag, New York, 1999Google Scholar
- 13.Toint, P.L.: Non-monotone filter methods. Presentation at the SIAM Conference on Optimization, Toronto, Canada, May 20–22, 2002Google Scholar
- 15.Ulbrich, M., Ulbrich, S., Vicente, L.N.: A globally convergent primal-dual interior-point filter method for nonconvex nonlinear programming. Technical Report TR00-12, Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005-1892, 2000 (Revised 2002)Google Scholar
- 16.Wächter, A., Biegler, L.T.: Global and local convergence of line search filter methods for nonlinear programming. CAPD Technical Report B-01-09, Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, 2001 (Revised 2002)Google Scholar