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An algorithm for solving the conditional extremum problemстатья
Статья опубликована в журнале из списка RSCI Web of Science
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из перечня ВАК
Дата последнего поиска статьи во внешних источниках: 7 декабря 2013 г.
- Авторы: Khapaev M.M., Tsygankov A.A.
- Журнал: Дифференциальные уравнения
- Том: 35
- Номер: 3
- Год издания: 1999
- Издательство: ФГБУ "Издательство "Наука"
- Местоположение издательства: Москва
- Первая страница: 310
- Последняя страница: 312
- Аннотация: The authors develop a method for investigating conditional extrema of a function. For the problem f(x)→inf, x∈X, X={x∈ℝ n :g i (x)=0, i=1,⋯,m}, where f(x), g 1 (x),⋯,g m (x) are continuously differentiable functions on X, a function of the form K(x,μ)=f(x)+∑ i=1 m μ i (x)g i -p i (x) is constructed, where the functions μ i (x) are regular in the considered domain and the p i are positive numbers; then the system of differential equations whose right-hand side is the antigradient of the function K(x,μ), namely, dx/dt=-K x (x,μ(x)),(1) is studied. The resultant system of differential equations has the singular manifolds described by the equations g i (x)=0, i=1,⋯,m. It is suggested to choose the function μ i (x) so that the integral curve achieves every manifold in finite time. The motion towards the extremum point is performed successively from one stable manifold to another, and after achieving a stable manifold, a trajectory remains on it. The aim of the paper is to construct particular systems of the form (1), by using of which the above described motion towards a local extremum of the function f is performed.
- Добавил в систему: Хапаев Михаил Михайлович