Globalizing stabilized sequential quadratic programming method by smooth primal-dual exact penalty function

Izmailov, A.F.; Solodov, M.V.; Uskov, E.I.

Статья опубликована в высокорейтинговом журнале

Информация о цитировании статьи получена из Web of Science, Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 9 июня 2016 г.

Авторы: Izmailov A.F., Solodov M.V., Uskov E.I.
Журнал: Journal of Optimization Theory and Applications
Том: 169
Номер: 1
Год издания: 2016
Издательство: Kluwer Academic/Plenum Publishers
Местоположение издательства: United States
Первая страница: 148
Последняя страница: 178
DOI: 10.1007/s10957-016-0889-y
Аннотация: An iteration of the stabilized sequential quadratic programming method consists in solving a certain quadratic program in the primal-dual space, regularized in the dual variables. The advantage with respect to the classical sequential quadratic programming is that no constraint qualifications are required for fast local convergence (i.e., the problem can be degenerate). In particular, for equality-constrained problems, the superlinear rate of convergence is guaranteed under the only assumption that the primal-dual starting point is close enough to a stationary point and a noncritical Lagrange multiplier (the latter being weaker than the second-order sufficient optimality condition). However, unlike for the usual sequential quadratic programming method, designing natural globally convergent algorithms based on the stabilized version proved quite a challenge and, currently, there are very few proposals in this direction. For equality-constrained problems, we suggest to use for the task linesearch for the smooth two-parameter exact penalty function, which is the sum of the Lagrangian with squared penalizations of the violation of the constraints and of the violation of the Lagrangian stationarity with respect to primal variables. Reasonable global convergence properties are established. Moreover, we show that the globalized algorithm preserves the superlinear rate of the stabilized sequential quadratic programming method under the weak conditions mentioned above. We also present some numerical experiments on a set of degenerate test problems.
Добавил в систему: Измаилов Алексей Феридович

	ИСТИНА	Войти в систему Регистрация
	ИПМех РАН
	Главная Поиск Статистика О проекте Помощь

ИСТИНА

ИПМех РАН

Globalizing stabilized sequential quadratic programming method by smooth primal-dual exact penalty functionстатья

Прикрепленные файлы