ДВОРIВНЕВI ЗАДАЧI ТА ДВОЕТАПНИЙ ПРОКСИМАЛЬНИЙ АЛГОРИТМ
DOI:
https://doi.org/10.17721/2706-9699.2021.2.07Ключові слова:
варiацiйна нерiвнiсть, задача про рiвновагу, дворiвнева задача, двоетапний проксимальний метод, збiжнiстьАнотація
У данiй роботi розглянуто дворiвневу задачу: варiацiйну нерiвнiсть на множинi розв’язкiв задачi про рiвновагу. Прикладом такої задачi є пошук нормальної рiвноваги Неша. Для розв’язання даної задачi запропоновано два алгоритми. Перший сумiщає у собi iдеї двоетапного проксимального методу та iтеративної регуляризацiї. А другий алгоритм є адаптивним варiантом першого з правилом оновлення параметрiв, що не використовує значень лiпшицевих констант бiфункцiї. Для монотонних бiфункцiй лiпшицевого типу та сильно монотонних лiпшицевих операторiв доведено теореми про сильну збiжнiсть алгоритмiв. Показано, що запропонованi алгоритми можна застосувати до монотонних дворiвневих варiацiйних нерiвностей в гiльбертових
просторах.
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