Conditioning of quasi-Newton methods for function minimization
Tóm tắt
Quasi-Newton methods accelerate the steepest-descent technique for function minimization by using computational history to generate a sequence of approximations to the inverse of the Hessian matrix. This paper presents a class of approximating matrices as a function of a scalar parameter. The problem of optimal conditioning of these matrices under an appropriate norm as a function of the scalar parameter is investigated. A set of computational results verifies the superiority of the new methods arising from conditioning considerations to known methods.
Từ khóa
Tài liệu tham khảo
Fletcher, R., 1963, A rapidly convergent descent method for minimization, Comput. J., 6, 163, 10.1093/comjnl/6.2.163
W. C. Davidon, Variable Metric Method for Minimization, Argonne National Laboratory Report ANL-5990, November 1959.
Broyden, C. G., 1965, A class of methods for solving nonlinear simultaneous equations, Math. Comp., 19, 577, 10.2307/2003941
Barnes, J. G. P., 1965, An algorithm for solving non-linear equations based on the secant method, Comput. J., 8, 66, 10.1093/comjnl/8.2.113
E. M. Rosen, "A review of quasi-Newton methods in nonlinear equation solving and unconstrained optimization," Nat. Conference of the ACM, Proceedings of the Twenty-First Conference, Thompson Book Co., Washington, D.C., 1966, pp. 37–41.
Zeleznik, Frank J., 1968, Quasi-Newton methods for nonlinear equations, J. Assoc. Comput. Mach., 15, 265, 10.1145/321450.321458
Box, M. J., 1966, A comparison of several current optimization methods, and the use of transformations in constrained problems, Comput. J., 9, 67, 10.1093/comjnl/9.1.67
A. Leon, A Comparison Among Eight Known Optimizing Procedures, Internal Working Paper No. 20, Space Sciences Laboratory, University of California, Berkeley, August 1964.
J. D. Pearson, On Variable Metric Methods of Minimization, Research Analysis Corp. Technical Paper, RAC-TP-302, February 1968.
Broyden, C. G., 1967, Quasi-Newton methods and their application to function minimisation, Math. Comp., 21, 368, 10.2307/2003239
Goldfarb, Donald, 1970, A family of variable-metric methods derived by variational means, Math. Comp., 24, 23, 10.2307/2004873