Acta Mathematicae Applicatae Sinica

, Volume 7, Issue 4, pp 354–362 | Cite as

Computation of a trust region step

  • Wu Shiquan 
  • Wu Fang 


The most time consuming work of the trust region method for unconstrained minimization is to compute a trust region step. This note tries to generalize the way of selecting a trust region and then to discuss how to compute a trust region step quickly.


Trust Region Math Application Region Method Region Step Trust Region Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    D.C. Sorensen, Nowton's Method with a Model Trust Region Modification,SIAM. J. Numer Anal.,19(2) (1982), 409–426.CrossRefGoogle Scholar
  2. [2]
    J.J. Moré and D.C. Sorensen, Computing a Trust Region Step,SIAM, J. Sci. Stat. Comput.,4(3) (1983), 553–572.Google Scholar
  3. [3]
    J.J. Moré, Recent Developments in Algorithms and Software for Trust Region Methods, in Mathematical Programming. The State of the art, Bonn, 1982, A. Bachem, M. Gröschel and B. Korte eds., Springer-Verlag.Google Scholar
  4. [4]
    M.D. Hebden, An Algorithm for Minimization Using Exact Second Derivatives, Atomic Energy Research Establishment, Report T.P. 515, Harewell, England, 1973.Google Scholar
  5. [5]
    N. Karmarkar, An Interior Point Approach to NP-Complete Problems (extended abstract), AT & T Bell Laboratories, Murray Hill, New Jersey 07974.Google Scholar
  6. [6]
    D.M. Gay, Computing Optimal Locally Constrained Step,SIAM. J. Sci. Stat. Comput.,2 (1981), 186–197.CrossRefGoogle Scholar
  7. [7]
    G.A. Shultz, R. B. Schnabel and R. H. Bryd, A Family of Trust-Region-Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties,SIAM. J. Numer. Anal.,22(1) (1985), 47–67.CrossRefGoogle Scholar
  8. [8]
    M.J.D. Powell, On the Global Convergence of Trust Region Algorithms for Unconstrained Minimization,Mathematical Programming,29 (1984), 297–303.Google Scholar
  9. [9]
    R.H. Byrd and R.B. Schnabel, Approximate Solution of the Trust Region Problem by Minimization over Two Dimensional Subspaces,Mathematical Programming,40 (1988), 247–263.CrossRefGoogle Scholar
  10. [10]
    C. Vande Panne, Methods for Linear and Quadratic Programming, Springer-Verlag, 1974.Google Scholar
  11. [11]
    R.K. Mecord, Minimization with One Linear Equality Constraint and Bounds on the Variables, Technical Report SOL 79–20, November 1977, Department of Operations Research, Stanford University.Google Scholar
  12. [12]
    P.E. Gill and W. Murray, Numerically Stable Methods for Quadratic Programming,Mathematical Programming,14(3) (1978), 349–372.CrossRefGoogle Scholar
  13. [13]
    P.M. Pardalos and N. Kovoor, An Algorithm for a Singly Constrained Class of Quadratic Programs Subject to Upper and Lower Bounds,Mathematical Programming,46 (1990), 321–328.CrossRefGoogle Scholar
  14. [14]
    Shiquan Wu, Restrict Step Size Method and its Extension,Acat Mathematicae Applicatae Sinica,12(1) (1989), 44–53 (in Chinese).Google Scholar
  15. [15]
    Shiquan Wu, Contribution à L'etude Numérique de Problémes D'optimisation, Thèse Doctorale, 1990, Université Paris I Pantheon-Sorbonne.Google Scholar

Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1991

Authors and Affiliations

  • Wu Shiquan 
    • 1
  • Wu Fang 
    • 1
  1. 1.Institute of Applied MathematicsAcademia SinicaBeijing

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