The BFGS method with exact line searches fails for non-convex objective functions

Mathematical Programming

Volumn 99, Issue 1, 2004, Pages 49-61

  Mascarenhas, Walter F ^a  

^a FEDERAL UNIVERSITY OF MATO GROSSO DO SUL   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; ITERATIVE METHODS; MATRIX ALGEBRA; OPTIMIZATION;

BFGS METHOD; LINE SEARCHES; NON-CONVEX OBJECTIVE FUNCTIONS; WOLFE CONDITIONS;

NONLINEAR PROGRAMMING;

EID: 21044434499     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-003-0421-7     Document Type: Article

References (8)

1. Yu-Hong, D.: Convergence properties of the BFGS Algorithm. SIAM J. Optim 13(3), 693-701 (2002)
2. Dixon, L.C.W.: Quasi-Newton Algorithms Generate Identical Points. Math. Program. 2, 383-387 (1972)
3. Fletcher, R., Powell, M.J.D.: A rapidly convergent descent method for minimization. Comput. J. 6, 163-168 (1963)
4. Hörmander, L.: The Analysis of Linear Partial Differential Operators I, Springer Verlag, 1983
5. Li, D., Fukushima, M.: On the Global Convergence of BFGS Method for Nonconvex Unconstrained Optimization. SIAM J. Optim. 11(4), 1054-1064 (2001)
6. Nocedal, J.: Theory of algorithms for unconstrained optimization. Acta Numerica 199-242 (1992)
7. Powell, M.J.D.: Nonconvex minimization calculations and the conjugate gradient method. In: D.F. Griffiths, ed., Numerical Analysis, Lecture Notes in Mathematics 1066, Springer Verlag, Berlin, 1984 pp. 122-141
8. Powell, M.J.D.: On the convergence of the DFP Algorithm for unconstrained optimization when there are only two variables. Math. Program. Ser. B. 87, 281-301 (2000)