A nonmonotone hybrid method for nonlinear systems

Optimization Methods and Software

Volumn 13, Issue 2, 2000, Pages 79-94

  Gasparo, Maria Grazia ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Global convergence; Hybrid methods; Nonlinear systems; Nonmonotone line search

Indexed keywords

EID: 0011530728     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/10556780008805776     Document Type: Article

References (23)

1. Bellavia, S., Gasparo, M. G. and Macconi, M. (1996). A Switching-Method for nonlinear systems. J. of Computational and Applied Mathematics, 71, 83-93.
2. Bellavia, S., Gasparo, M. G. and Macconi, M. (1996). Partially updated Switching-Method for systems of nonlinear equations. J. of Computational and Applied Mathematics, 76, 77-88.
3. Bogle, I. D. L. and Perkins, J. D. (1990). A new sparsity preserving quasi-Newton update for solving nonlinear equations. SIAM J. Sci. Stat. Comput., 11, 621-630.
4. Bouaricha, A. and Schnabel, R. B. (1997). Algorithm 768: TENSOLVE: A Software Package for Solving Systems of Nonlinear Equations and Nonlinear Least-Squares Problems Using Tensor Methods. ACM Transactions on Mathematical Software, 23, 174-195.
5. Conn, A. R. and Scheinberg, K. Ph.L. (1997). Toint Recent progress in unconstrained nonlinear optimization without derivatives. Math. Programming, 79, 397,414.
6. Dennis, J. E., Jr. and Schnabel, R. B. (1983). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, NJ.
7. Ferris, M. C. and Lucidi, S. (1994). Nonmonotone stabilization methods for nonlinear equations. J. of Optimization Theory and Applications, 81, 53-71.
8. Friedlander, A., Gomes-Ruggiero, M. A., Kozakevich, D. N., Martinez, J. M. and Santos, S. A. (1997). Solving nonlinear systems of equations by means quasi-Newton methods with a nonmonotone strategy. Optimization Methods and Software, 8, 25-51.
9. Gasparo, M. G. (1998). A nonmonotone hybrid method for nonlinear systems: the complete numerical results, Technical report 98/5, Dipartimento di Energetica, Universita' di Firenze, Italia.
10. Gomez-Ruggiero, M. A., Martinez, J. M. and Moretti, A. C. (1992). Comparing algorithms for solving sparse nonlinear systems of equations. SIAM J. on Sci. Stat. Comput., 13, 459-483.
11. Grippo, L., Lampariello, F. and Lucidi, S. (1986). A nonmonotone line search technique for Newton's method. SIAM J. Numer. Anal., 23, 707-716.
12. Grippo, L., Lampariello, F. and Lucidi, S. (1991). A class of nonmonotone Stabilization Methods in Unconstrained Optimization. Numerische Mathematik, 59, 779-805.
13. Li, G. (1989). Successive column correction algorithms for solving sparse nonlinear systems of equations. Math. Programming, 43, 187-207.
14. Luksan, L. (1994). Inexact Trust Region Method for Large Sparse Systems of Nonlinear Equations. J. on Opt. Theory and Appl., 81, 569-590.
15. Moré, J. J. and Cosnard, M. Y. (1979). Numerical solution of nonlinear equations. ACM Trans. on Math. Software, 5, 64-85.
16. Moré, J. J., Garbow, B. S. and Hillstrom, K. E. (1981). Testing Unconstrained Optimization Software. ACM Trans. on Math. Software, 7, 17-41.
17. Polak, P. (1971). Computational Methods in Optimization: A Unified Approach. Ac. Press, N.Y.
18. Polak, E. (1976). On the Global Stabilization of Locally Convergent Algorithms. Automatica, 12, 337-342.
19. Spedicato, E. and Huang, Z. (1996). Numerical experience with Newton-like methods for nonlinear algebraic systems. Tech. Rep. Dip. M.S.I. Appl., 15.
20. Toint, Ph. L. (1986). Numerical Solution of Large Sets of Algebraic Nonlinear Equations. Math. of Comput., 46, 175-189.
21. Toint, Ph. L. (1996). An assessment of non-monotone line-search techniques for unconstrained minimization. SIAM J. on Sci. Comput., 17, 725-739.
22. Torczon, V. (1997). On the convergence of pattern search algorithms. SIAM J. Optim., 7, 1-25.
23. Wright, M. H. (1996). Direct search methods: Once scorned, now respectable in: D. F. Griffiths and G. A. Watson eds Proceedings of the 1995 Dundee Biennal Conference in Numerical Analysis Addison-Wesley, reading, MA and Longman, Harlow, UK.