A globalization procedure for solving nonlinear systems of equations

Numerical Algorithms

Volumn 12, Issue 2, 1996, Pages 273-286

  Shi, Yixun ^a  

^a BLOOMSBURG UNIVERSITY   (United States)

Author keywords

Descent methods; Global convergence; Newton's method; Nonlinear system of equations; Step length

Indexed keywords

EID: 21344439758     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02142807     Document Type: Article

References (15)

1. L. Armijo, Minimization of functions having Lipschitz continuous first partial derivatives, Pacific J. Math. 16 (1966) 1-3.
2. R.W. Chamberlain, C. Lemaréchal, H. Pedersen and M.J.D. Powell, The watchdog technique for forcing convergence in algorithms for constrained optimization, Math. Programming Stud. 16 (1982) 1-17.
3. A.R. Conn, N.I.M. Gould and P. Toint, A globally convergent augmented lagrangian algorithm for optimization with general constraints and simple bounds, SIAM J. Numer. Anal. 28 (1991) 545-572.
4. J.R. Dennis, Jr. and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983.
5. S.C. Eisenstat and H.F. Walker, Globally convergent inexact Newton methods, SIAM J. Optimization 4 (1994) 393-422.
6. R. Fletcher, Practical Methods of Optimization, Wiley, 1987.
7. E.P. Gill, W. Murray, A.M. Saunders and H.M. Wright, A note on a sufficient-decrease criterion for a non-derivative step-length procedure, Math. Programming 23 (1982) 349-352.
8. A.A. Goldstein, On steepest descent, SIAM J. On Control 3 (1965) 147-151.
9. A.A. Goldstein, Constructive Real Analysis, Harpers & Row, New York, 1967.
10. M.A. Gomes-Ruggiero, J.M. Martínez and A.C. Moretti, Comparing algorithms for solving sparse nonlinear systems of equations, SIAM J. Sci. Stat. Comput. 13 (1992) 459-483.
11. A. Griewank, Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation, Optimization Methods and Software 1 (1992) 35-54.
12. R. Noubary and Y. Shi, A method for parameter estimation of a non-linear signal, linear filter and autocorrelated noise, J. Applied Statistical Science, to appear.
13. F.A. Potra and Y. Shi, An efficient line search algorithm for unconstrained optimization, J. Optimization Theory and Application, to appear.
14. M.J.D. Powell, Some global convergence properties of a variable metric algorithm for minimization without exact line searches, SIAM-AMS Proceedings, Vol. 9, eds. R.W. Cottle and C.E. Lemke, SIAM Publications, Philadelphia, 1976.
15. P. Wolfe, Convergence conditions for ascent methods, SIAM Review 11 (1968) 226-235.