On the convergence of the DFP algorithm for unconstrained optimization when there are only two variables

Mathematical Programming, Series B

Volumn 87, Issue 2, 2000, Pages 281-301

  Powell, M J D ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Convergence theory; Unconstrained optimization; Variable metric algorithms

Indexed keywords

EID: 0043263288     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101070050115     Document Type: Article

References (8)

1. Davidon, W.C. (1959): Variable metric method for minimization. Report ANL 5990 (revised), Argonne National Laboratory, Illinois, USA
2. Dixon, L.C.W. (1972): Quasi-Newton algorithms generate identical points. Math. Program. 2, 383-387
3. Fletcher, R., Powell, M.J.D. (1963): A rapidly convergent descent method for minimization. Comput. J. 6, 163-168
4. Polak, E., Ribière, G. (1969): Note sur la convergence de methodes de directions conjuguées. Rev. Française Informat. Recherche Opérationelle 16, 35-43
5. Powell, M.J.D. (1970): A new algorithm for unconstrained optimization. In: Rosen, J.B., Mangasarian, O.L., Ritter, K., eds., Nonlinear Programming, 1970. Academic Press, New York, pp. 31-65
6. Powell, M.J.D. (1972): Some properties of the variable metric algorithm. In: Lootsma, F.A., ed., Numerical Methods for Nonlinear Optimization, 1971. Academic Press, London, pp. 1-17
7. Powell, M.J.D. (1984): Nonconvex minimization calculations and the conjugate gradient method. In: Griffiths, D.F., ed., Numerical Analysis Proceedings, 1983 (Lecture Notes in Mathematics 1066). Springer-Verlag, Berlin, pp. 122-141
8. Wolfe, P. (1970): Convergence theory in nonlinear programming. In: Abadie, J., ed., Integer and Nonlinear Programming, 1969. North-Holland, Amsterdam, pp. 1-36