Numerische Mathematik

, Volume 70, Issue 4, pp 515–539 | Cite as

On the convergence of a new trust region algorithm

  • Ya-xiang Yuan


In this paper we present a new trust region algorithm for general nonlinear constrained optimization problems. The algorithm is based on the\(L_\infty\) exact penalty function. Under very mild conditions, global convergence results for the algorithm are given. Local convergence properties are also studied. It is shown that the penalty parameter generated by the algorithm will be eventually not less than the \(l_1\) norm of the Lagrange multipliers at the accumulation point. It is proved that the method is equivalent to the sequential quadratic programming method for all large \(k\), hence superlinearly convergent results of the SQP method can be applied. Numerical results are also reported.

Mathematics Subject Classification (1991):65K05, 49D37 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Ya-xiang Yuan
    • 1
  1. 1.Computing Center, Academia Sinica, P.O. Box 2719, Beijing 10080, China CN

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