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The theory of 2-regularity for mappings with Lipschitzian derivatives and its applications to optimality conditionsстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 29 мая 2015 г.
- Авторы: Izmailov A.F., Solodov M.V.
- Журнал: SIAM Journal on Optimization
- Том: 27
- Номер: 3
- Год издания: 2002
- Издательство: Society for Industrial and Applied Mathematics
- Местоположение издательства: United States
- Первая страница: 614
- Последняя страница: 635
- DOI: 10.1287/moor.27.3.614.308
- Аннотация: We study local structure of a nonlinear mapping near points where standard regularity and/or smoothness assumptions need not be satisfied. We introduce a new concept of 2-regularity (a certain kind of second-order regularity) for a once differentiable mapping whose derivative is Lipschitz continuous. Under this 2-regularity condition, we obtain the representation theorem and the covering theorem (i.e., stability with respect to “right-hand side” perturbations) under assumptions that are weaker than those previously employed in the literature for results of this type. These results are further used to derive a constructive description of the tangent cone to a set defined by (2-regular) equality constraints and optimality conditions for related optimization problems. The class of mappings introduced and studied in the paper appears to be a convenient tool for treating complementarity structures by means of an appropriate equation-based reformulation. Optimality conditions for mathematical programs with (equivalently reformulated) complementarity constraints are also discussed.
- Добавил в систему: Измаилов Алексей Феридович
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Полный текст | 7697c73780_article.pdf | 172,2 КБ | 14 ноября 2012 [izmaf] |