ДВОЕТАПНI ПРОКСИМАЛЬНI АЛГОРИТМИ ДЛЯ ЗАДАЧ ПРО РIВНОВАГУ В ПРОСТОРАХ АДАМАРА
DOI:
https://doi.org/10.17721/2706-9699.2024.2.01Ключові слова:
простiр Адамара, задача про рiвновагу, псевдомонотоннiсть, проксимальний алгоритм, збiжнiстьАнотація
В статтi розглянуто задачi про рiвновагу в метричних
просторах Адамара. Отримана теорема про слабку збiжнiсть двоетапного проксимального алгоритму для псевдомонотонних задач рiвноважного програмування в просторах Адамара. Запропоновано адаптивний двоетапний проксимальний алгоритм для
задач в метричних просторах Адамара. 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. Запропоновано та теоретично обгрунтовано адаптивний екстрапроксимальний алгоритм. Запропоновано та теоретично обгрунтовано регуляризований адаптивний екстрапроксимальний алгоритм. Для
регуляризацiї базової екстрапроксимальної схеми було використано класичну схему Гальперна. Для псевдомонотонних бiфункцiй лiпшицевого типу доводиться теорема про збiжнiсть. Показано, що запропонованi алгоритм можна застосувати до псевдомонотонних варiацiйних нерiвностей в гiльбертових просторах.
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