Алгоритм для задачі про рівновагу у банаховому просторі
DOI:
https://doi.org/10.17721/2706-9699.2025.1.05Ключові слова:
збiжнiсть, задача про рiвновагу, псевдомонотоннiсть, проксимальний алгоритмАнотація
В статтi розглянуто задачi про рiвновагу в 2-рiвномiрно опуклих та рiвномiрно гладких банахових просторах. Отримана теорема про слабку збiжнiсть двоетапного проксимального алгоритму для псевдомонотонних задач рiвноважного програмування в 2-рiвномiрно опуклих та рiвномiрно гладких банахових просторах. Запропоновано адаптивний двоетапний проксимальний алгоритм для задач про рiвновагу. Правило оновлення параметрiв не використовує значень лiпшицевих констант бiфункцiї та на вiдмiну вiд правил типу лiнiйного пошуку не потребує обчислень значень бiфункцiї в додаткових точках. Для псевдомонотонних бiфункцiй лiпшицевого типу доведена теорема про слабку збiжнiсть породжених алгоритмом послiдовностей.
Посилання
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