Abstract.
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 [8]. 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 [8].
Similar content being viewed by others
References
Bertsekas, D.P.: Constrained optimization and Lagrange multiplier methods. Computer Science and Applied Mathematics, Academic Press Inc., New York, 1982
Boggs, P.T., Tolle, J.W.: Sequential quadratic programming. In: Acta numerica, Acta Numer., Cambridge Univ. Press, Cambridge, 1995, pp. 1–51
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, 2001
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, 2000
Facchinei, F., Lucidi, S.: Quadratically and superlinearly convergent algorithms for the solution of inequality constrained minimization problems. J. Optim. Theory Appl. 85, 265–289 (1995)
Fletcher, R., Gould, N.I.M., Leyffer, S., Toint, P.L., Wächter, A.: Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming. SIAM J. Optim. 13, 635–659 (2002)
Fletcher, R., Leyffer, S.: Nonlinear programming without a penalty function. Math. Program. 91, 239–269 (2002)
Fletcher, R., Leyffer, S., Toint, P.L.: On the global convergence of a filter–SQP algorithm. SIAM J. Optim. 13, 44–59 (2002)
Glad, T., Polak, E.: A multiplier method with automatic limitation of penalty growth. Math. Program. 17, 140–155 (1979)
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)
Lucidi, S.: New results on a continuously differentiable exact penalty function. SIAM J. Optim. 2, 558–574 (1992)
Nocedal, J., Wright, S.J.: Numerical optimization. Springer Series in Operations Research, Springer-Verlag, New York, 1999
Toint, P.L.: Non-monotone filter methods. Presentation at the SIAM Conference on Optimization, Toronto, Canada, May 20–22, 2002
Ulbrich, M., Ulbrich, S.: Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function. Math. Program. 95, 103–135 (2003)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Additional information
Mathematics Subject Classification (2000): 90C55, 65K05, 90C30
Rights and permissions
About this article
Cite this article
Ulbrich, S. On the superlinear local convergence of a filter-SQP method. Math. Program., Ser. B 100, 217–245 (2004). https://doi.org/10.1007/s10107-003-0491-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10107-003-0491-6