Convergence property of a class of variable metric methods

Applied Mathematics Letters

Volumn 17, Issue 4, 2004, Pages 437-442

  Zhang, Zhong Zhi ^a   Cao, Ding Hua ^b   Zeng, Jin Ping ^b  

^a HUNAN CITY UNIVERSITY   (China)

^b HUNAN UNIVERSITY   (China)

Author keywords

Quadratic function; Variable metric methods

Indexed keywords

FUNCTIONS; ITERATIVE METHODS; LINEAR EQUATIONS; MATRIX ALGEBRA; PROBLEM SOLVING; THEOREM PROVING; VECTORS;

BROYDEN CLASS; GLOBAL CONVERGENCE; HESSIAN MATRIX; QUADRATIC FUNCTION; QUASI NEWTON MATRICES; VARIABLE METRIC METHODS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 1842790117     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(04)90086-9     Document Type: Article

References (10)

1. M.J.D. Powell, On the convergence of the variable metric algorithm, Journal of the Institute of Applied Methods 7, 21-36, (1971).
2. L.C.W. Dixon, Quasi-Newton algorithms generate identical points, Mathematical Programming 2, 383-387, (1972).
3. R. Byrd and J. Nocedal, A tool for analysis of quasi-Newton methods with application to unconstrained minimization, SIAM Journal on Numerical Analysis 26, 727-739, (1989).
4. R. Byrd, J. Nocedal and Y. Yuan, Global convergence of a class of quasi-Newton methods with application to unconstrained minimization, SIAM Journal on Numerical Analysis 24, 1171-1190, (1987).
5. M.J.D. Powell, Some global convergence properties of a variable metric algorithm for minimization without exact line search, In Nonlinear Programming, SIAM-AMS Proceedings, Volume IX, (Edited by R.W. Cottle and C.E. Lemke), SIAM, Philadelphia, PA, (1976).
6. D.H. Li, On the global convergence of DFP method, Journal of Hunan University 20 (2), 16-20, (1993).
7. M.J.D. Powell, On the convergence of the DFP algorithm for unconstrained optimization when there are only two variables, Mathematical Programming 87, 281-301, (2000).
8. D.G. Pu and W. Yu, On the global convergence property of DFP algorithm, Annals of Operations Research 24, 175-184, (1990).
9. J.E. Dennis, Jr. and J.J. Moré, Quasi-Newton methods, motivation and theory, SIAM Review 19, 46-89, (1977).
10. J.J. Moré, and A. Trangenstein, On the global convergence of Broyden's method, Mathematics of Computation 30, 523-540, (1976).