Mathematical Programming

, Volume 87, Issue 2, pp 215–249

A primal-dual trust-region algorithm for non-convex nonlinear programming

  • Andrew R. Conn
  • Nicholas I. M. Gould
  • Dominique Orban
  • Philippe L. Toint

DOI: 10.1007/s101070050112

Cite this article as:
Conn, A., Gould, N., Orban, D. et al. Math. Program. (2000) 87: 215. doi:10.1007/s101070050112


A new primal-dual algorithm is proposed for the minimization of non-convex objective functions subject to general inequality and linear equality constraints. The method uses a primal-dual trust-region model to ensure descent on a suitable merit function. Convergence is proved to second-order critical points from arbitrary starting points. Numerical results are presented for general quadratic programs.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Andrew R. Conn
    • 1
  • Nicholas I. M. Gould
    • 2
  • Dominique Orban
    • 3
  • Philippe L. Toint
    • 4
  1. 1.IBM T.J. Watson Research Center, P.O.Box 218, Yorktown Heights, NY, USA, e-mail:
  2. 2.Rutherford Appleton Laboratory, Computational Science and Engineering Departement, Chilton, Oxfordshire, England, e-mail:
  3. 3.CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 1, France, e-mail: Dominique.Orban@cerfacs.frFR
  4. 4.Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium, e-mail:

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