Quasi-Newton trust region algorithm for non-smooth least squares problems

Applied Mathematics and Computation

Volumn 105, Issue 2-3, 1999, Pages 183-194

  Sun, W ^a   Sampaio, R J B ^b   Yuan, J ^b  

^a NANJING NORMAL UNIVERSITY   (China)

^b FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

Author keywords

Convergence; Non smooth least squares problems; Non smooth optimization; Trust region method

Indexed keywords

EID: 0347536850     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(98)10103-0     Document Type: Article

References (26)

1. X. Chen, T. Yamamoto, On the convergence of some quasi-Newton methods for nonlinear equations with nondifferentiable operators, Computing 49 (1992) 87-94.
2. J.E. Dennis, R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983.
3. R. Fletcher, An algorithm for solving linearly constrained optimization problems, Mathematical Programming 2 (1972) 133-165.
4. R. Fletcher, Practical Methods of Optimization, vol 2, Wiley, New York, 1981.
5. S.P. Han, J.S. Pang, N. Rangaraj, Globally convergent Newton methods for nonsmooth equations, Math. Oper. Res. 17 (1992) 586-607.
6. C.T. Kelly, Identification of the support of nonsmoothness, in: W.W. Hanger, D.W. Hearn, P.M. Pardalos (Eds.), Large Scale Optimization, State of the Art, Kluwer, Boston, 1994, pp. 192-205.
7. B. Kummer, Newton's method based on generalized nonsmooth functions: convergence analysis, in: W. Oettli, D. Pallaschke (Eds.), Advance in Optimization, Springer, Berlin, 1992, pp. 171-194.
8. J.M. Martinez, M.C. Zambaldi, Least change update methods for nonlinear systems with nondifferential terms, Numer. Func. Anal. Optim. 14 (1993) 405-415.
9. J.J. Moré, The Levenberg-Marquardt algorithm: implementation and theory, in: G.A. Watson (Ed.), Proceeding of the Dundee Conference on Numerical Analysis, Springer, 1978.
10. J.J. Moré, Recent developments in algorithms and software for trust region methods, in: A. Bachern, M. Grötschel, B. Korte (Eds.), Mathematical Programming, The State of the Art, Springer, Berlin, Bonn, 1983, pp. 258-287.
11. M.J.D. Powell, Convergence properties of a class of minimization algorithms, in: O.L. Mangasarian, R.L. Meyer, S.M. Robinson (Eds.), Nonlinear Programming 2, Academic Press, New York, 1975, pp. 1-27.
12. L. Qi, Convergence analysis of some algorithms for nonsmooth equations, Mathematics of Operations Research 18 (1993) 227-244.
13. L. Qi, Trust region algorithms for solving nonsmooth equations, SIAM J. Optimization 5 (1995) 219-230.
14. L. Qi, J. Sun, A nonsmooth version of Newton's method, Math. Programming 58 (1993) 353-368.
15. L. Qi, W. Sun, An iterative method for the minimax problem, in: D.Z. Du, P.M. Pardalos (Eds.), Minimax and Applications, Kluwer, Boston, USA, 1995, pp. 55-67.
16. R. Sampaio, W. Sun, J. Yuan, Trust region algorithm for nonsmooth optimization, Applied Mathematics and Computation 85 (1997) 109-116.
17. D.C. Sorensen, Newton's method with a modal trust region modification, SIAM J. Numerical Analysis 19 (1982) 409-426.
18. W. Sun, Generalized Newton's method for LC1 unconstrained optimization, Journal of Computational Mathematics 13 (1995) 250-258.
19. W. Sun, Newton's method and quasi-Newton-SQP method for general LC1 constrained optimization, Applied Mathematics and Computation 92 (1998) 69-84.
20. W. Sun, On non-quadratic model optimization methods, Asia Pacific Journal of Operations Research 13 (1996) 43-63.
21. W. Sun, S. Di, Trust region method for conic model to solve unconstrained optimization, Optimization Methods and Software 6 (1996) 237-263.
22. R. Sampaio, W. Sun, J. Yuan, On trust region method for nonsmooth optimization, Applied Mathematics and Computation 85 (1997) 109-116.
23. W. Sun, Y. Yuan, Optimization Theory and Methods, Science Press, Beijing, China, 1997.
24. Y. Yuan, Conditions for convergence of trust region algorithms for nonsmooth optimization, Mathematical Programming 31 (1985) 220-228.
25. P.P. Zabreiko, D.F. Nguyen, The majorant method in the theory of Newton-Kantorovich approximations and the Pták error estimates, in: Numerical Functional Analysis and Optimization, 1987, pp. 671-684.
26. A.I. Zincenko, Some approximation methods of solving equations with nondifferentiable operator, Ukrainian, Dopovidi Akad. Nauk. Ukrain. RSR (1963) 156-161.