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DOI: 10.46698/e7204-1864-5097-s
Алгоритм нелинейной вязкости с возмущением для нерасширяющих многозначных отображений
Сахеби Х. Р.
Владикавказский математический журнал. 2021. Том 23. Выпуск 1.С.60-76.
Аннотация: Итерационные алгоритмы вязкости для поиска общего элемента множества неподвижных точек нелинейных операторов и множества решений вариационных неравенств исследовались многими авторами. Соответствующая техника позволяет применить этот метод к выпуклой оптимизации, линейному программированию и монотонным включениям. В этой статье на основе метода вязкости с возмущением, мы вводим новый алгоритм нелинейной вязкости для нахождения элемента множества неподвижных точек нерасширющих многозначных отображений в гильбертовом пространстве. Установлены теоремы о сильной сходимости этого алгоритма при подходящих предположениях относительно параметров. Наши результаты можно рассматривать как обобщение и усиление имеющихся в текущей литературе результатов. Представлены также некоторые числовые примеры, показывающие эффективность и применитость предложенного алгоритма.
Ключевые слова: проблема неподвижной точки, обобщенного проблема равновесия, нерасширяющее многозначное отображение, гильбертово пространство
Образец цитирования: Sahebi, H. R. Nonlinear Viscosity Algorithm with Perturbation for Nonexpansive Multi-Valued Mappings // Владикавк. мат. журн. 2020. Т. 23, № 1. С. 60-76 (in English). DOI 10.46698/e7204-1864-5097-s
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