Step-size estimation for unconstrained optimization methods

Computational and Applied Mathematics

Volumn 24, Issue 3, 2005, Pages 399-416

  Shi, Zhen Jun ^a,b   Shen, Jie ^c  

^a QUFU NORMAL UNIVERSITY   (China)

^b INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

^c UNIVERSITY OF MICHIGAN DEARBORN   (United States)

Author keywords

Convergence; Descent methods; Step size estimation; Unconstrained optimization

Indexed keywords

CONVERGENCE; CONVERGENCE PROPERTIES; DESCENT METHOD; LINE SEARCHES; NUMERICAL EXPERIMENTS; OPTIMIZATION METHOD; SIZE ESTIMATION; STEP SIZE; STEP-SIZE ESTIMATION; UNCONSTRAINED OPTIMIZATION;

OPTIMIZATION;

EID: 34247548302     PISSN: 22383603     EISSN: 18070302     Source Type: Journal    
DOI: 10.1590/s1807-03022005000300005     Document Type: Article

References (26)

1. [1] L. Armijo, Minimization of function having Lipschitz continuous first partial derivatives, Pacific J. Math , 16 (1966), 1–13.
2. [2] J. Barzilai and J.M. Borwein, Two-point step size gradient methods, IMA J. Numer. Anal., 8 (1988), 141–148.
3. [3] E.G. Birgin and J. M. Martinez, A spectral conjugate gradient method for unconstrained optimization, Appl. Math. Optim., 43 (2001), 117–128.
4. [4] A. I. Cohen, Stepsize analysis for descent methods, J. Optim. Theory Appl., 33(2) (1981), 187–205.
5. [5] H. B. Curry, The method of steepest descent for non-linear minimization problems, Quart. Appl. Math., 2 (1944), 258–261.
6. [6] Y. H. Dai and L. Z. Liao, R-linear convergence of the Barzilai and Borwein gradient method, IMA J. Numer. Anal., 22 (2002), 1–10.
7. [7] R. Fletcher, The Barzilai Borwein method-steepest descent method resurgent? Report in the International Workshop on “Optimization and Control with Applications”, Erice, Italy, July (2001), 9–17.
8. [8] A. V. Fiacco, G. P. McCormick, Nonlinear programming: Sequential Unconstrained Minimization Techniques, SIAM, Philadelphia, (1990).
9. [9] L. Grippo and S. Lucidi, Aglobally convergent version of the Polak-Ribiere conjugate gradient, Math. Prog., 78 (1997), 375–391.
10. [10] A. A. Goldstein, Cauchy’s method of minimization, Numer. Math. 4 (1962), 146–150.
11. [11] A. A. Goldstein, On steepest descent, SIAM J. Control, 3 (1965), 147–151.
12. [12] A. A. Goldstein, J. F. Price, An effective algorithm for minimization, Numer. Math., 10 (1967), 184–189.
13. [13] J. J. Moré, B. S. Garbow and K. E. Hillstrom, Testing unconstrained optimization software, ACM Trans. Math. Software, 7 (1981), 17–41.
14. [14] J. Nocedal and J. S. Wright, Numerical Optimization, Springer-Verlag NewYork, Inc. (1999).
15. [15] J. Nocedal, Theory of algorithms for unconstrained optimization, Acta Numerica, 1 (1992), 199–242.
16. [16] M. J. D. Powell, Direct search algorithms for optimization calculations, Acta Numerica, 7 (1998), 287–336.
17. [17] E. Polak, Optimization: Algorithms and Consistent Approximations, Springer, New York, (1997).
18. [18] M. J. D. Powell, Restart procedure for the conjugate gradient method, Math. Prog., 12 (1977), 241–254.
19. [19] M. Raydan and B. F. Svaiter, Relaxed steepest descent and Cauchy-Barzilai- Borwein method, Comput. Optim. Appl., 21 (2002), 155–C167.
20. [20] M. Raydan, The Barzilai and Borwein method for the large scale unconstrained minimization problem, SIAM J. Optim., 7 (1997), 26–33.
21. [21] M. Raydan, On the Barzilai Borwein gradient choice of steplength for the gradient method, IMA J. Numer. Anal., 13 (1993), 321–326.
22. [22] Z. J. Shi, Restricted PR conjuate gradient method and its convergence(in Chinese), Advances in Mathematics, 31(1) (2002), 47–55.
23. [23] P. Wolfe, Convergence condition for ascent methods II: some corrections, SIAM Rev., 13 (1971), 185–188.
24. [24] P. Wolfe, Convergence condition for ascent methods, SIAM Rev., 11 (1969), 226–235.
25. [25] Y. Yuan and W. Y. Sun, Optimization Theory and Methods, Science Press, Beijing (1997).
26. [26] Y. Yuan, Numerical Methods for Nonlinear Programming, Shanghai Scientific & Technical Publishers, (1993).