Convergence of Broyden-like matrix

Applied Mathematics Letters

Volumn 11, Issue 5, 1998, Pages 35-37

  Li, Donghui ^a   Zeng, Jinping ^a   Zhou, Shuzi ^a  

^a HUNAN UNIVERSITY   (China)

Author keywords

Broyden like matrix; Convergence; Nonlinear equations; Nonlinear programming

Indexed keywords

EID: 0042045480     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(98)00076-7     Document Type: Article

References (9)

1. C.G. Broyden, J.E. Dennis, Jr. and J.J. Moré, On the local and superlinear convergence of quasi-Newton methods, J. Inst. Math. Appl. 12, 223-236, (1973).
2. A. Griewank, The 'global' convergence of Broyden-like methods with a suitable line search, J. Austrialian Math. Soc. Ser. B 28, 75-92, (1986).
3. D. Li, Global convergence of nonsingular Broyden's methods for solving unconstrained optimizations, Chinese J. Numer. Math. Appl. 17, 85-94, (1995).
4. S. Zhou, D. Li and J. Zeng, A successive approximation quasi-Newton process for nonlinear complementarity problem, In Recent Advances in Nonsmooth Optimization, (Edited by D.-Z. Du, L. Qi and R. Womersley), pp. 459-472, World Scientific Publishers, (1995).
5. J. J. Moré and A. Trangenstein, On the global convergence of Broyden's method, Math. Prog. 30, 523-540, (1976).
6. A.R. Conn, N.I.M. Gould and Ph.L. Toint, Convergence of quasi-Newton matrices generated by the symmetric rank one update, Math. Prog. 50, 177-195, (1991).
7. M.J.D. Powell and R.-P. Ge, The convergence of variable metric matrix in unconstrained optimization, Math. Prog. 27, 123-143, (1983).
8. J. Stoer, The convergence of matrix generated by rank-2 methods from the restricted β-class of Broyden, Numer. Math. 44, 37-52, (1984).
9. J.E. Dennis, Jr. and J.J. Moré, A characterization of superlinear convergence to quasi-Newton methods, Math. Comp. 126, 549-560, (1974).