Modified by conjugate directions method of numerical minimization of multivariable function for data analysis problems
DOI:
https://doi.org/10.15587/1729-4061.2010.2642Keywords:
minimization method, conjugate directions methodAbstract
Some modifications of conjugate directions methods for functions minimization are constructed. The introduction of parameters and additional information about properties of the function allows ensuring convergence condition and speed.References
- Нікольський Ю.В. Невизначеність та надлишковість даних у моделі процесу їх аналізу / Ю.В.Нікольський // Східно-Європейський журнал передових технологій. – Харків, 2009. – № 6/2 (42). – С. 27-31.
- Яковлев М.Н. О некоторых методах решения нелинейных уравнений / Яковлев М.Н. // Труды математического ин-та АН СССР, 84, 1975. – С. 8-43.
- Davidon W.C. Variable Metric Method for Minimization / Davidon W.C. // A.E.C. Research and Development Report, ANL-5990, 1959. – P.1-27.
- Fletcher R. A rapidly convergent descent method for minimization / Fletcher R., Powell M. // Comput. J. – 1963. – Vol.7. – P. 163-168.
- McCormick G. P. Variable metric methods and unconstrained optimization/ McCormick G. P., Pearson J. D. // Proceedings of the Joint Conference on Optimization/ University of Keele. – 1968. – March. – P. 154-158.
- Pearson J.D. Variable metric methods of minimization / Pearson J.D. // Comput J. – 1969. – Vol.12, №2. – P. 171–181.
- Cohen A. Rate of coversgance for root finging and optimization algorithms: Ph. D. Dissertation / University of California Berkeley; Cohen A. // Полак Е. Численные методы оптимизации/ Полак Е. – М.: Мир, 1974. – С.43-49.
- Полак Б.Т. Метод сопряженных градиентов / Полак Б.Т. // Труды второй школы по матем. прогр. и смежным вопросам. – Вып. 1. – М., 1969. – С. 152–202.
- Майстровский Г.Д. О сходимости метода сопряженных градиентов/ Майстровский Г.Д.// ЖВМ и МФ. – 1971. – Вип.11, №5. – C.1291–1294.
- Смоляк С.А. Квадратичная сходимость метода сопряженных градиентов/ Смоляк С.А. // Труды 111 зимней школы по математическому программированию/ МИСИ. – М., 1970. – С.134-143.
- Huang H.Y. Unitied approach to quadratically convergent algoritmus for function minimization / Huang H.Y. // JoTA. – 1970. – Vol.5, №6. – P.405-425.
- Powell M. J. D. On the convergence of the variable metric algoritm / Powell M. J. D. // Report T.P. / AERE, Harwell, England. – 1970. – №382. – Р.148-156.
- Полак Е. Численные методы оптимизации. Единый поход / Полак Е. – М.: Мир, 1974.
- Данилин Ю.М. Методы сопряженных направлений для решения задач минимизации / Данилин Ю.М. // Кібернетика. – 1971. – №5. – С.37-43.
- Пшеничный Б.Н. Численные методы в экстремальных задачах / Пшеничный Б.Н., Данилин Ю.М. – М.: «Наука», 1975. – 319 с.
- Данилин Ю.М. Скорость сходимоcти методов сопряженных направлений / Данилин Ю.М. // Кібернетика. – 1977. – №6. – С.24-37.
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