Global Convergence of a Nonmonotone Trust Region Algorithm with Memory for Unconstrained Optimization

  • Zhensheng Yu
  • Anqi Wang


In this paper, we consider a trust region algorithm for unconstrained optimization problems. Unlike the traditional memoryless trust region methods, our trust region model includes memory of the past iteration, which makes the algorithm less myopic in the sense that its behavior is not completely dominated by the local nature of the objective function, but rather by a more global view. The global convergence is established by using a nonmonotone technique. The numerical tests are also given to show the efficiency of our proposed method.


Trust region Memory model Nonmonotone technique Global convergence 

Mathematics Subject Classifications (2010)

65K05 90C30 


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  1. 1.
    Powell, M.J.D.: In: Mangasarian, O.L.M., Meyer, R.R., Robinson, S.M. (eds.) Convergence properties of a class minimization algorithms in nonlinear programming, vol. 2, pp. 47–67 (1975)Google Scholar
  2. 2.
    Powell, M.J.D.: On global convergence of trust region algorithms for unconstrained optimization. Math. Program. 29, 297–303 (1984)MATHCrossRefGoogle Scholar
  3. 3.
    Yuan, Y.X.: Nonlinear Optimization: Trust Region Algorithms. Research Report, Institute of Computational Mathematics, Chinese Academy of Sciences (1999)Google Scholar
  4. 4.
    Sorensen, D.C.: Trust region methods for unconstrained optimization. In: Powell, M.J.D. (ed.) Nonlinear Optimization 1981, pp. 29–38. Academic, London (1982)Google Scholar
  5. 5.
    Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust Region Methods. MSP-SIAM Series on Optimization. Philadelphia, PA (2000)Google Scholar
  6. 6.
    Gould, N.I.M., Lucidi, S., Roma, M., Toint, P.L.: A line search algorithm with memory for unconstrained optimization. In: De leone, R., Mauli, A., Pardalos, P., Toraldo, G. (eds.) High Performance Algorithms and Software in Nonlinear Optimization, pp. 207–223. Kluwer Academic Publishers (1998)Google Scholar
  7. 7.
    Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search technique for Newton’s method. SIAM J. Numer. Anal. 23, 707–716 (1986)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Deng, N.Y., Xiao, Y., Zhou, F.: Nonmonotone trust region algorithm. J. Optim. Theory. Appl. 76, 259–285 (1993)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Ke, X.W., Han, J.Y.: A class of nonmonotone trust region algorithm for unconstrained optimization. Sci. China 28, 488–492 (1998)Google Scholar
  10. 10.
    Toint, P.L.: A nonmonotone trust region algorithm for nonlinear programming subject to convex constraints. Math. Program. 77, 69–94 (1997)MathSciNetMATHGoogle Scholar
  11. 11.
    Chen, Z.W., Han, J.Y., Xu, D.C.: A nonmonotone trust region algorithm for nonlinear programming with simple bound constraints. Appl. Math. Optim. 43, 63–85 (2000)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Bongartz, I., Conn, A.R., Gould, N.I., Toint, P.L.: CUTE: constrained and unconstrained testing environments. ACM T Math. Software. 21, 123–160 (1995)MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.College of ScienceUniversity of Shanghai for Science and TechnologyShanghaiPeople’s Republic of China

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