A derivative-free nonmonotone line-search technique for unconstrained optimization

Journal of Computational and Applied Mathematics

Volumn 219, Issue 2, 2008, Pages 383-397

  Diniz Ehrhardt, M A ^a   Martinez J M ^a   Raydan, M ^b  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b FACULTAD DE CIENCIAS   (Venezuela)

Author keywords

Derivative free methods; Nonmonotone line search schemes; SR1 updates; Unconstrained minimization

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; CURVE FITTING; FINITE DIFFERENCE METHOD; FUNCTION EVALUATION; INFORMATION ANALYSIS; LEARNING ALGORITHMS; OPTIMIZATION;

CONVERGENCE PROPERTIES; DIRECT SEARCH ALGORITHM; ELSEVIER (CO); FINITE DIFFERENCE (FD); LINE SEARCHES; NUMERICAL EXPERIMENTS; OBJECTIVE FUNCTION (OF); SEARCH TECHNIQUES; TYPE METHODS; UNCONSTRAINED MINIMIZATION; UNCONSTRAINED OPTIMIZATION;

GRADIENT METHODS;

EID: 46749084262     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.07.017     Document Type: Article

References (30)

1. Alberto P., Nogueira F., Rocha H., and Vicente L.N. Pattern search methods for user-provided points: application to molecular geometry problems. SIAM J. Opt. 14 (2004) 1216-1236
2. Allaire G. Shape Optimization by the Homogenization Method (2001), Springer, New York
3. Barzilai J., and Borwein J.M. Two point step size gradient methods. IMA J. Numer. Anal. 8 (1988) 141-148
4. Van den Berghen F., and Bersini H. CONDOR, a new parallel, constrained extension of Powell's UOBYQA algorithm: experimental results and comparison with the DFO algorithm. J. Comput. Appl. Math. 181 (2005) 157-175
5. Birgin E.G., Martínez J.M., and Raydan M. Inexact spectral gradient method for convex-constrained optimization. IMA J. Numer. Anal. 23 (2003) 539-559
6. Brezinski C., and Matos A.C. A derivation of extrapolation algorithms based on error estimates. J. Comput. Appl. Math. 66 (1996) 5-26
7. C. Brezinski, M. Redivo Zaglia, Extrapolation Methods, Theory and Practice, North-Holland, Amsterdam, 1991.
8. Broyden C.G. Quasi-Newton methods and their application to function minimization. Math. Comput. 21 (1967) 368-381
9. Byrd R.H., Khalfan H.F., and Schnabel R.B. Analysis of a rank-one trust region method. SIAM J. Opt. 6 (1996) 1025-1039
10. Conn A.R., Gould N.I.M., and Toint P.L. Convergence of quasi-Newton matrices generated by the symmetric rank one update. Math. Programming 50 (1991) 177-195
11. Conn A.R., Scheinberg K., and Toint Ph.L. Recent progress in unconstrained nonlinear optimization without derivatives. Math. Programming 79 (1997) 397-414
12. A. L. Custódio, J. E. Dennis Jr., L. N. Vicente, Using simplex gradients of nonsmooth functions in direct search methods, IMA J. Numer., to appear.
13. Davidon W.C. Variance algorithms for minimization. Comput. J. 10 (1968) 406-410
14. Dennis Jr. J.E., and Schnabel R.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1983), Prentice-Hall, Englewood Cliffs, NJ
15. Diniz-Ehrhardt M.A., Gomes-Ruggiero M.A., Lopes V.L.R., and Martínez J.M. Discrete Newton's method with local variations and global convergence for nonlinear equations. Optimization 52 (2003) 417-440
16. Fiacco A.V., and McCormick G.P. Nonlinear Programming: Sequential Unconstrained Minimization Techniques (1968), Wiley, New York
17. Fletcher R. Practical Methods of Optimization (1987), Wiley, New York
18. Gilmore P., and Kelley C.T. An implicit filtering algorithm for optimization of functions with many local minima. SIAM J. Opt. 5 (1995) 269-285
19. Grippo L., Lampariello F., and Lucidi S. A nonmonotone line search technique for Newton's method. SIAM J. Numer. Anal. 23 (1986) 707-716
20. Haslinger J., and Mäckinen R.A.E. Introduction to Shape Optimization: Theory, Approximation, and Computation (2003), SIAM, Philadelphia, PA
21. Kolda T.G., Lewis R.M., and Torczon V. Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45 (2003) 385-482
22. La Cruz W., Martínez J.M., and Raydan M. Spectral residual method without gradient information for solving large-scale nonlinear systems of equations. Math. Comput. 75 (2006) 1449-1466
23. Li D.H., and Fukushima M. A derivative-free line search and global convergence of Broyden-like method for nonlinear equations. Opt. Methods Software 13 (2000) 181-201
24. Lucidi S., and Sciandrone M. On the global convergence of derivative-free methods for unconstrained optimization. SIAM J. Opt. 13 (2002) 97-116
25. Mohammadi B., and Pironneau O. Applied Shape Optimization for Fluids (2001), Clarendon Press, Oxford
26. Moré J.J., Garbow B.S., and Hillstrom K.E. Testing unconstrained optimization software. ACM Trans. Math. Software 7 (1981) 17-41
27. Powell M.J.D. Direct search algorithms for optimization calculations. Acta Numer. 7 (1998) 287-336
28. Powell M.J.D. On trust region methods for unconstrained minimization without derivatives. Math. Progamming 97 (2003) 605-623
29. Powell M.J.D. On the use of quadratic models in unconstrained minimization without derivatives. Opt. Methods Software 19 (2004) 399-411
30. Raydan M. The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Opt. 7 (1997) 26-33