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On the convergence, invariance, and related aspects of a modification of Huang’s algorithm. (English) Zbl 0462.65042

MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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[1] Huang, H. Y.,Unified Approach to Quadratically Convergent Algorithms for Function Minimization, Journal of Optimization Theory and Applications, Vol. 5, pp. 405-423, 1970. · Zbl 0194.19402 · doi:10.1007/BF00927440
[2] Dixon, L. C. W.,Quasi-Newton Algorithms Generate Identical Points, Mathematical Programming, Vol. 2, pp. 383-387, 1972. · Zbl 0245.65029 · doi:10.1007/BF01584554
[3] Dixon, L. C. W.,Quasi-Newton Techniques Generate Identical Points, II, Proof of Four New Theorems, Mathematical Programming, Vol. 3, pp. 345-358, 1972. · Zbl 0252.90053 · doi:10.1007/BF01585007
[4] Spedicato, E.,Stability of Huang’s Update for the Conjugate Gradient Method, Journal of Optimization Theory and Applications, Vol. 11, pp. 469-479, 1973. · Zbl 0254.49034 · doi:10.1007/BF00935660
[5] Powell, M. J. D.,On the Convergence of Variable-Metric Algorithms, Journal of the Institute of Mathematics and Applications, Vol. 7, pp. 21-36, 1971. · Zbl 0217.52804 · doi:10.1093/imamat/7.1.21
[6] Powell, M. J. D.,Some Properties of the Vartable-Metric Algorithms, Numerical Methods for Nonlinear Optimization, Edited by F. Lootsma, Academic Press, London, England, 1972.
[7] Jacobson, D. H., andOksman, W.,An Algorithm that Minimizes Homogeneous Functions of M Variables in N + 2 Iterations and Rapidly Minimizes General Functions, Journal of Mathematical Analysis and Applications, Vol. 38, pp. 535-552, 1972. · Zbl 0234.65063 · doi:10.1016/0022-247X(72)90067-4
[8] Jacobson, D. H., andPels, L. M.,A Modified Homogeneous Algorithm for Function Minimization, Journal of Mathematical Analysis and Applications, Vol. 46, pp. 533-541, 1974. · Zbl 0279.65049 · doi:10.1016/0022-247X(74)90259-5
[9] Kowalik, J. S., andRamakrishnan, K. G.,A Numerically Stable Optimization Method Based on a Homogeneous Function, Mathematical Programming, Vol. 11, pp. 50-66, 1976. · Zbl 0351.90052 · doi:10.1007/BF01580370
[10] Spedicato, E.,A Variable-Metric Method for Function Minimization Derived from Invariance to Nonlinear Scaling, Journal of Optimization Theory and Applications, Vol. 20, pp. 315-329, 1976. · Zbl 0316.90066 · doi:10.1007/BF00933626
[11] Spedicato, E.,Recent Development in the Variable-Metric Method for Nonlinear Unconstrained Optimization, Toward Global Optimization, Edited by L. C. W. Dixon and G. P. Szegö, North-Holland, Amsterdam, Holland, 1978.
[12] Boland, W. R., Kamgania, E. R., andKowalik, J. S.,A Conjugate Gradient Optimization Method Invariant to Nonlinear Scaling, Journal of Optimization Theory and Applications, Vol. 22, pp. 221-230, 1979. · Zbl 0396.49024 · doi:10.1007/BF00933228
[13] Kowalik, J. S., Kamgania, E. R., andBloand, W. R.,An Exponential Function as a Model for Conjugate Gradient Optimization Method, Journal of Mathematical Analysis and Applications, Vol. 67, pp. 476-482, 1979. · Zbl 0416.65045 · doi:10.1016/0022-247X(79)90037-4
[14] Avriel, M.,Nonlinear Programming, Prentice Hall, Englewood Cliffs, New Jersey, 1976.
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