On the convergence of a trust-region method for solving constrained nonlinear equations with degenerate solutions

Journal of Optimization Theory and Applications

Volumn 123, Issue 1, 2004, Pages 187-211

  Tong, X J ^a   Qi, L ^b  

^a CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

Constrained nonlinear equations; error bound; global convergence; superlinear quadratic convergence; trust region methods

Indexed keywords

SET THEORY;

CLOSED CONVEX SETSS; CONSTRAINED NONLINEAR EQUATION; CONTINUOUSLY DIFFERENTIABLE; ERROR BOUND; GLOBAL CONVER-GENCE; LOCAL ERROR; QUADRATIC CONVERGENCE; SUPERLINEAR; SUPERLINEAR/QUADRATIC CONVERGENCE; TRUST-REGION METHODS;

NONLINEAR EQUATIONS;

EID: 5444256857     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOTA.0000043997.42194.dc     Document Type: Article

References (21)

1. YAMASHITA, N., and FUKUSHIMA, M., On the Rate of Convergence of the Levenberg-Marquardt Method, Computing (Supplement), Vol. 15, pp. 239-249, 2001.
2. FAN, J., and YUAN, Y., On the Convergence of a New Levenberg-Marquardt Method, Report, Institute of Computational Mathematics and Scientific/ Engineering Computing, Chinese Academy of Science, Beijing, China, 2001.
3. EL-HAWARY, M. E., Optimal Power Flow: Solution Techniques, Requirements, and Challenges, IEEE Service Center, Piscataway, New Jersey, 1996.
4. WOOD, A. J., and WOLLENBERG, B. F., Power Generation, Operation, and Control, John Wiley and Sons, New York, NY, 1996.
5. CHIANG, H. D., and FEKIH-AHMED, L., Quasi-Stability Regions of Nonlinear Dynamical Systems: Optimal Estimations, IEEE Transactions on Circuits and Systems, Vol. 43, pp. 636-643, 1996.
6. CHIANG, H. D., HIRSCH, M. W., and WU, F. F., Stability Regions of Nonlinear Autonomous Dynamical Systems, IEEE Transactions on Automatic Control, Vol. 33, pp. 16-27, 1988.
7. BELLAVIA, S., MACCONI, M., and MORINI, B., An Affine Scaling Trust-Region Approach to Bound-Constrained Nonlinear Systems, Technical Report, Dipartmento di Energetica, University of Florence, Florence, Italy, 2001.
8. GABRIEL, S. A., and PANG, J. S., A Trust-Region Method for Constrained Nonsmooth Equations, Large-Scale Optimization: State of the Art, Edited by W. W. Hager, D. W. Hearn, and P. M. Pardalos, Kluwer Academic Publishers, Boston, Massachusetts, pp. 159-186, 1994.
9. KANZOW, C., An Active-Set Type Newton Method for Constrained Nonlinear Equations, Complementarity: Applications, Algorithms, and Extensions, Edited by M. C. Ferris, O. L. Mangasarian, and J. S. Pang, Kluwer Academic Publishers, Dordrecht, Holland, pp. 179-200, 2001.
10. KANZOW, C., Strictly Feasible Equation-Based Method for Mixed Complementarity Problems, Numerische Mathematik, Vol. 89, pp. 135-160, 2001.
11. KANZOW, C., YAMASHITA, N., and FUKUSHIMA, M., Leveberg-Marquardt Methods for Constrained Nonlinear Equations with Strong Local Convergence Properties, Technical Report 2002-2007, Department of Applied Mathematics and Physics, Kyoto University, Kyoto, Japan, 2002.
12. KOZAKEVICH, D. N., MARTINEZ, J. M., and SANTOS, S. A., Solving Nonlinear Systems of Equations with Simple Bounds, Journal of Computational and Applied Mathematics, Vol. 16, pp. 215-235, 1997.
13. MONTEIRO, R. D. C., and PANG, J. S., A Potential Reduction Newton Method for Constrained Equations, SIAM Journal on Optimization, Vol. 9, pp. 729-754, 1999.
14. QI, L., TONG, X. J., and LI, D. H., An Active-Set Projected Trust-Region Algorithm for Box-Constrained Nonsmooth Equations, Journal of Optimization Theory and Applications, Vol. 120, 2004.
15. ULBRICH, M., Nonmonotone Trust-Region Method for Bound-Constrained Semi-smooth Equations with Applications to Nonlinear Mixed Complementarity Problems, SIAM Journal on Optimization, Vol. 11, pp. 889-917, 2001.
16. DAN, H., YAMASHITA, N., and FUKUSHIMA, M., Convergence Properties of the Inexact Levenberg-Marquardt Method under Local Error Bound Conditions, Optimization Methods and Software, Vol. 17, pp. 605-626, 2002.
17. TSENG, P., Error Bounds and Superlinear Convergence Analysis of Some Newton-Type Methods in Optimization, Nonlinear Optimization and Related Topics, Edited by G. Di Pillo and F. Giannessi, Kluwer Academic Publishers, Boston, Massachusetts, pp. 445-462, 2000.
18. STEIHAUG, T., The Conjugate Gradient Method and Trust Region in Large-Scale Optimization, SIAM Journal on Numerical Analysis, Vol. 20, pp. 626-637, 1983.
19. YUAN, Y., On the Truncated Conjugate Gradient Method, Mathematical Programming, Vol. 87, pp. 561-573, 2000.
20. H. JIANG, H., and QI, L., A New Nonsmooth Equations Approach to Nonlinear Complementarity Problems, SIAM Journal on Control and Optimization, Vol. 35, pp. 178-193, 1997.
21. HOCK, W., and SCHITTKOWSKI, K., Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, Germany, Vol. 187, 1981.