\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

A non-monotone retrospective trust-region method for unconstrained optimization

Abstract Related Papers Cited by
  • In this paper, a new non-monotone trust-region algorithm is proposed for solving unconstrained nonlinear optimization problems. We modify the retrospective ratio which is introduced by Bastin et al. [Math. Program., Ser. A (2010) 123: 395-418] to form a convex combination ratio for updating the trust-region radius. Then we combine the non-monotone technique with this new framework of trust-region algorithm. The new algorithm is shown to be globally convergent to a first-order critical point. Numerical experiments on CUTEr problems indicate that it is competitive with both the original retrospective trust-region algorithm and the classical trust-region algorithms.
    Mathematics Subject Classification: 90C30, 90C26, 65K05.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    F. Bastin, V. Malmedy, M. Mouffe, Ph. L. Toint and D. Tomanos, A retrospective trust-region method for unconstrained optimization, Mathematical Programming, 123 (2010), 395-418.doi: 10.1007/s10107-008-0258-1.

    [2]

    I. Bongartz, A. R. Conn, N. I. M. Gould and Ph. L. Toint, CUTE: Constrained and Unconstrained Testing Environment, ACM Transactions on Mathematical Software, 21 (1995), 123-160.doi: 10.1145/200979.201043.

    [3]

    R. M. Chamberlain, M. J. D. Powell, C. Lemaréchal and H. C. Pedersen, The watchdog technique for forcing convergence in algorithms for constrained optimization, Mathematical Programming Studies, 16 (1982), 1-17.

    [4]

    J. Chen, W. Y. Sun and R. J. B. de Sampaio, Numerical research on the sensitivity of nonmonotone trust region algorithms to their parameters, Computers and Mathematics with Applications, 56 (2008), 2932-2940.doi: 10.1016/j.camwa.2008.05.010.

    [5]

    A. R. Conn, N. I. M. Gould and Ph. L. Toint, "Trust-Region Methods,'' MPS/SIAM Series on Optimization, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA; Mathematical Programming Society (MPS), Philadelphia, PA, 2000.doi: 10.1137/1.9780898719857.

    [6]

    N. Y. Deng, Y. Xiao and F. J. Zhou, Nonmonotonic trust region algorithm, Journal of Optimization Theory and Applications, 76 (1993), 259-285.doi: 10.1007/BF00939608.

    [7]

    E. D. Dolan and J. J. Moré, Benchmarking optimization software with performance profiles, Mathematical Programming, Series A, 91 (2002), 201-213.doi: 10.1007/s101070100263.

    [8]

    J. H. Fu and W. Y. Sun, Nonmonotone adaptive trust-region method for unconstrained optimization problems, Applied Mathematics and Computation, 163 (2005), 489-504.doi: 10.1016/j.amc.2004.02.011.

    [9]

    N. I. M. Gould, D. Orban and Ph. L. Toint, CUTEr and SifDec: A Constrained and Unconstrained Testing Environment, revisited, ACM Transactions on Mathematical Software, 29 (2003), 373-394.doi: 10.1145/962437.962438.

    [10]

    L. Grippo, F. Lampariello and S. Lucidi, A nonmonotone line search technique for newton's method, SIAM Journal on Numerical Analysis, 23 (1986), 707-716.doi: 10.1137/0723046.

    [11]

    J. T. Mo, C. Y. Liu and S. C. Yan, A nonmonotone trust region method based on nonincreasing technique of weighted average of the successive function values, Journal of Computational and Applied Mathematics, 209 (2007), 97-108.doi: 10.1016/j.cam.2006.10.070.

    [12]

    J. J. Moré, Recent developments in algorithms and software for trust region methods, in "Mathematical Programming: The State of the Art" (eds. A. Bachem, M. Grötschel and B. Korte), Springer, Berlin, (1983), 258-287.

    [13]

    J. J. Moré and D. C. Sorensen, Computing a trust region step, SIAM Journal on Scientific and Statistical Computing, 4 (1983), 553-572.doi: 10.1137/0904038.

    [14]

    J. Nocedal and S. J. Wright, "Numerical Optimization,'' $2^{nd}$ edition, Springer Series in Operations Research and Financial Engineering, Springer, New York, 2006.

    [15]

    M. J. D. Powell, A hybrid method for nonlinear equations, in "Numerical Methods for Nonlinear Algebraic Equations" (ed. P. Rabinowitz), Gordon and Breach, London, (1970), 87-114.

    [16]

    M. J. D. Powell, Convergence properties of a class of minimization algorithms, in "Nonlinear Programming, 2" (eds. O. L. Mangasarian, R. R. Meyer and S. M. Robinson), Academic Press, London, (1974), 1-27.

    [17]

    G. A. Shultz, R. B. Schnabel and R. H. Byrd, A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties, SIAM Journal on Numerical Analysis, 22 (1985), 47-67.doi: 10.1137/0722003.

    [18]

    W. Y. Sun, Nonmonotone trust region method for solving optimization problems, Applied Mathematics and Computation, 156 (2004), 159-174.doi: 10.1016/j.amc.2003.07.008.

    [19]

    W. Y. Sun, J. Y. Han and J. Sun, Global convergence of nonmonotone descent methods for unconstrained optimization problems, Journal of Computational and Applied Mathematics, 146 (2002), 89-98.doi: 10.1016/S0377-0427(02)00420-X.

    [20]

    W. Y. Sun and Y. X. Yuan, "Optimization Theory and Methods. Nonlinear Programming,'' Springer Optimization and Its Applications, Vol. 1, Springer, New York, 2006.

    [21]

    W. Y. Sun and Q. Y. Zhou, An unconstrained optimization method using nonmonotone second order Goldstein's line search, Science in China Series A: Mathematics, 50 (2007), 1389-1400.doi: 10.1007/s11425-007-0072-x.

    [22]

    Ph. L. Toint, An assessment of nonmonotone linesearch techniques for unconstrained optimization, SIAM Journal on Scientific Computing, 17 (1996), 725-739.doi: 10.1137/S106482759427021X.

    [23]

    Ph. L. Toint, A non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints, Mathematical Programming, 77 (1997), 69-94.doi: 10.1007/BF02614518.

    [24]

    Y. X. Yuan, On the convergence of trust region algorithms, (in Chinese) Mathematica Numerica Sinica, 16 (1994), 333-346.

    [25]

    Y. X. Yuan and W. Y. Sun, "Optimization Theory and Methods,'' (in Chinese) Science Press, Beijing, 1997.

    [26]

    H. C. Zhang and W. W. Hager, A nonmonotone line search technique and its application to unconstrained optimization, SIAM Journal on Optimization, 14 (2004), 1043-1056.doi: 10.1137/S1052623403428208.

    [27]

    D. T. Zhu, A nonmonotone trust region technique for unconstrained optimization problems, Systems Science and Mathematical Sciences, 11 (1998), 375-382.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(93) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return