ДВОРІВНЕВІ ЗАДАЧІ ТА ДВОЕТАПНИЙ ПРОКСИМАЛЬНИЙ АЛГОРИТМ
DOI:
https://doi.org/10.17721/2706-9699.2023.2.01Ключові слова:
варiацiйна нерiвнiсть, задача про рiвновагу, двоетапний проксимальний метод, iтеративна регуляризацiя, сильна збiжнiстьАнотація
У статтi розглядається дворiвнева задача: варiацiйна нерiвнiсть на множинi розв’язкiв задачi про рiвновагу. Для розв’язання задачi запропоновано алгоритм, що сумiщає у собi iдеї двоетапного проксимального методу та iтеративної регуляризацiї. Крiм того, дослiджено адаптивний варiант алгоритму 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.
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