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

@article{Conn2000APT,
  title={A primal-dual trust-region algorithm for non-convex nonlinear programming},
  author={Andrew R. Conn and Nicholas I. M. Gould and Dominique Orban and Philippe L. Toint},
  journal={Math. Program.},
  year={2000},
  volume={87},
  pages={215-249}
}
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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