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Non Monotone Algorithms for Unconstrained Minimization: Upper Bounds on Function Values

  • U. M. Garcia-Palomares
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 199)

Abstract

Non monotone algorithms allow a possible increase of function values at certain iterations. This paper gives a suitable control on this increase to preserve the convergence properties of its monotone counterpart. A new efficient MultiLineal Search is also proposed for minimization algorithms.

keywords

Non Monotone Lineal Search Trust Region 

References

  1. [1]
    B. Addis, S. Leiffer. A trust region algorithm for global optimization. Preprint ANL/MCS-Pl190-0804, Argonne National Laboratory, Il, USA, 2004.Google Scholar
  2. [2]
    A.R. Conn, N.I.M. Gould, P.L. Toint. Trust region methods. MPS-SIAM Series on Optimization, Philadelphia, ISBN 0-89871-460-5, 2000.Google Scholar
  3. [3]
    J.E. Dennis, J.J. Moré. A characterization of superlinear convergence and its application to quasi-Newton methods. Mathematics of Computation 28:549–560, 1974.MathSciNetCrossRefGoogle Scholar
  4. [4]
    U.M. García-Palomares, F.J. González-Castaño, J.C. Burguillo-Rial. A combined global & local search (CGLS) approach to global optimization. Journal of Global Optimization To appear, 2006.Google Scholar
  5. [5]
    U.M. García-Palomares, J.F. Rodríguez. New sequential and parallel derivative-free algorithms for unconstrained optimization. SIAM Journal on Optimization 13:79–96, 2002.MathSciNetCrossRefGoogle Scholar
  6. [6]
    N.I.M. Gould, D. Orban, Ph.L. Toint. GALAHAD a library of thread-safe Fortran 90 packages for large scale nonlinear optimization. Transactions of the ACM on Mathematical Software 29-4:353–372, 2003.MathSciNetCrossRefGoogle Scholar
  7. [7]
    N.I.M. Gould, C. Sainvitu, Ph.L. Toint. A filter-trust-region method for unconstrained minimization. Report 04/03, Rutherford Appleton Laboratory, England, 2004.Google Scholar
  8. [8]
    L. Grippo, F. Lampariello, S. Lucidi. A nonmonotone line search technique for Newton’s method. SIAM Journal Numerical Analysis 23-4:707–716, 1986.MathSciNetCrossRefGoogle Scholar
  9. [9]
    L. Grippo, M. Sciandrone. Nonmonotone globalization techniques for the Barzilai-Borwein gradient method. Computational Optimization and Applications 23:143–169, 2002.MathSciNetCrossRefGoogle Scholar
  10. [10]
    C. Gurwitz, L. Klein, M. Lamba. A MATLAB library of test functions for unconstrained optimization. Report 11/94, Brooklin College, USA, 1994.Google Scholar
  11. [11]
    W.W. Hager. Minimizing a quadratic over a sphere. SIAM Journal on Optimization 12:188–208, 2001.MATHMathSciNetCrossRefGoogle Scholar
  12. [12]
    J. Han, J. Sun, W. Sun. Global convergence of non-monotone descent methods for unconstrained optimization problems. Journal of Computational and Applied Mathematics 146-1:89–98, 2002.MathSciNetGoogle Scholar
  13. [13]
    P.D. Hough, J.C. Meza. A class of trust region methods for parallel optimization. SIAM Journal on Optimization 13-1:264–282, 2002.MathSciNetCrossRefGoogle Scholar
  14. [14]
    C.T. Kelley. Iterative methods for optimization. SIAM Frontiers in Applied Mathematics ISBN 0-89871-433-8, 1999.Google Scholar
  15. [15]
    S. Lucidi, M. Sciandrone. On the global convergence of derivative free methods for unconstrained optimization. SIAM Journal on Optimization 13-1:119–142, 2002.Google Scholar
  16. [16]
    V.P. Plagianakos, G.D. Magoulas, M.N. Vrahatis. Deterministic nonmonotone strategies for effective training of multilayer perceptrons. IEEE Transactions on Neural Networks 13-6:1268–1284, 2002.CrossRefGoogle Scholar
  17. [17]
    M. Raydan. The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM Journal on Optimization 7:26–33, 1997.MATHMathSciNetCrossRefGoogle Scholar
  18. [18]
    M. Rojas, S. Santos, D. Sorensen. LSTRS: Matlab software for large-scale trust-region subproblems and regularization. Technical Report 2003-4, Department of mathematics, Wake Forest University, NC, USA, 2003.Google Scholar
  19. [19]
    P.L. Toint. An assesment of non-monotone linesearch techniques for unconstrained optimization. SIAM Journal on Scientific and Statistical Computing 8-3:416–435, 1996.Google Scholar
  20. [20]
    P.L. Toint. Non-monotone trust region algorithms for nonlinear optimization subject to convex constraints. Mathematical Programming 77:69–94, 1997.MATHMathSciNetCrossRefGoogle Scholar
  21. [21]
    J.L. Zhang, X.S. Zhang. A modified SQP method with nonmonotone linesearch technique. Journal of Global Optimization 21:201–218, 2001.CrossRefGoogle Scholar

Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • U. M. Garcia-Palomares
    • 1
  1. 1.Dep Procesos y SistemasUniversidad Simón BolívarCaracasVenezuela

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