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On variable-metric algorithms. (English) Zbl 0203.48703

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[1] Davidon, W. C.,Variable-Metric Method for Minimization, Argonne National Laboratory, Report No. ANL-5990, 1959. · Zbl 0752.90062
[2] Hestenes, M. R., andStiefel, E.,Methods of Conjugate Gradients for Solving Linear Systems, Journal of Research of the National Bureau of Standards, Vol. 49, No. 6, 1952. · Zbl 0048.09901
[3] Broyden, C. G.,Quasi-Newton Methods and Their Application to Function Minimization, Mathematics of Computation, Vol. 21, No. 99, 1967. · Zbl 0155.46704
[4] Fletcher, R., andReeves, C. M.,Function Minimization by Conjugate Gradients, Computer Journal, Vol. 7, No. 2, 1964. · Zbl 0132.11701
[5] Shah, B. V., Bueher, R. J., andKempthorne, O.,Some Algorithms for Minimizing a Function of Several Variables, SIAM Journal on Applied Mathematics, Vol. 12, No. 1, 1964.
[6] Zoutendijk, G.,Method of Feasible Directions, American Elsevier Publishing Company, New York, 1960. · Zbl 0097.35408
[7] Fletcher, R., andPowell, M. J. D.,A Rapidly Convergent Descent Method for Minimization, Computer Journal, Vol. 6, No. 2, 1963. · Zbl 0132.11603
[8] Goldfarb, D.,Sufficient Conditions for the Convergence of Variable-Metric Algorithm, Optimization, Edited by R. Fletcher, Academic Press, New York, 1969. · Zbl 0249.65044
[9] Pearson, J. D.,On Variable-Metric Methods of Minimization, Computer Journal, Vol. 12, No. 2, 1969. · Zbl 0207.17301
[10] Greenstadt, J.,Variations on the Variable-Metric Methods, Mathematics of Computation, Vol. 24, No. 109, 1970. · Zbl 0204.49601
[11] Goldfarb, D.,A Family of Variable-Metric Methods Derived by Variational Means, Mathematics of Computation, Vol. 24, No. 109, 1970. · Zbl 0196.18002
[12] Huang, H. Y.,Unified Approach to Quadratically Convergent Algorithms for Function Minimization, Journal of Optimization Theory and Applications, Vol. 5, No. 6, 1970. · Zbl 0184.20202
[13] Huang, H. Y., andLevy, A. V.,Numerical Experiments on Quadratically Convergent Algorithms for Function Minimization, Journal of Optimization Theory and Applications, Vol. 6, No. 3, 1970. · Zbl 0187.40401
[14] Powell, M. J. D.,An Iterative Method for Finding Stationary Values of a Function of Several Variables, Computer Journal, Vol. 5, No. 2, 1962. · Zbl 0104.34303
[15] Fletcher, R.,A Review of Methods for Unconstrained Optimization, Optimization, Edited by R. Fletcher, Academic Press, New York, 1969. · Zbl 0194.20404
[16] Penrose, R.,A Generalized Inverse for Matrices, Proceedings of the Cambridge Philosophical Society, Vol. 51, Part 3, 1954. · Zbl 0065.24603
[17] Murtagh, B. A., andSargent, R. W. H.,A Constrained Minimization Method with Quadratic Convergence, Optimization, Edited by R. Fletcher, Academic Press, New York, 1969. · Zbl 0214.42401
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