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A variable metric-method for function minimization derived from invariancy to nonlinear scaling. (English) Zbl 0316.90066

MSC:
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49Kxx Optimality conditions
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[1] Broyden, C. G.,Quasi-Newton Methods and Their Application to Function Minimization, Mathematics of Computation, Vol. 21, No. 99, 1967. · Zbl 0155.46704
[2] Bard, Y.,On a Numerical Instability of Davidon-Like Methods, Mathematics of Computation, Vol. 22, No. 105, 1968. · Zbl 0165.50303
[3] Oren, S. S.,Self-Scaling Variable Metric Algorithms for Unconstrained Minimization, Stanford University, PhD Thesis, 1972.
[4] Huang, H. Y.,Unified Approach to Quadratically Convergent Algorithms for Function Minimization, Journal of Optimization Theory and Applications, Vol. 5, No. 5, 1970. · Zbl 0184.20202
[5] Davison, E. J., andWong, P.,A Robust Algorithm that Minimizes L-functions, University of Toronto, Control Systems Report No. 7313, 1973.
[6] Spedicato, E., Computing Center, CISE, Segrate, Milano, Italy, Report No. CISE-N-175, 1975.
[7] Fried, I.,N-Step Conjugate Gradient Minimization Scheme for Nonquadratic Functions, AIAA Journal, Vol. 9, No. 11, 1971. · Zbl 0235.65040
[8] Oren, S. S., andSpedicato, E.,Optimal Conditioning of Self-Scaling Variable Metric Method, Mathematical Programming, Vol. 10, No. 1, 1976. · Zbl 0342.90045
[9] Spedicato, E.,A Bound on the Condition Number of Rank-Two Corrections and Applications to the Variable-Metric Method, Calcolo, Vol. 12, No. 2, 1975. · Zbl 0318.65029
[10] Stoer, J.,On the Convergence Behaviour of Some Minimization Algorithms, Proceedings of the IFIP Conference, Stockholm, Sweden, 1974. · Zbl 0295.65044
[11] Spedicato, E.,On Condition Numbers in Rank-Two Minimization Algorithms, Towards Global Minimization, Edited by L. C. W. Dixon and G. P. Szego, North-Holland Publishing Company, Amsterdam, Holland, 1975. · Zbl 0339.90053
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