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

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Abstract.

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.

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Authors and Affiliations

  1. IBM T.J. Watson Research Center, P.O.Box 218, Yorktown Heights, NY, USA, e-mail: arconn@watson.ibm.com, , , , , , US

    Andrew R. Conn

  2. Rutherford Appleton Laboratory, Computational Science and Engineering Departement, Chilton, Oxfordshire, England, e-mail: n.gould@rl.ac.uk, , , , , , GB

    Nicholas I. M. Gould

  3. CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 1, France, e-mail: Dominique.Orban@cerfacs.fr, , , , , , FR

    Dominique Orban

  4. Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium, e-mail: Philippe.Toint@fundp.ac.be, , , , , , BE

    Philippe L. Toint

Authors
  1. Andrew R. Conn
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  2. Nicholas I. M. Gould
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  3. Dominique Orban
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  4. Philippe L. Toint
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Received: July 19, 1999 / Accepted: February 1, 2000¶Published online March 15, 2000

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Conn, A., Gould, N., Orban, D. et al. A primal-dual trust-region algorithm for non-convex nonlinear programming. Math. Program. 87, 215–249 (2000). https://doi.org/10.1007/s101070050112

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  • DOI: https://doi.org/10.1007/s101070050112

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