Thuật toán dạng FR để tìm nghiệm xấp xỉ cho các phương trình toán tử phi tuyến đồng monotone

Arabian Journal of Mathematics - Tập 10 - Trang 261-270 - 2021
Auwal Bala Abubakar1,2, Kanikar Muangchoo3, Abdulkarim Hassan Ibrahim4, Jamilu Abubakar4,5, Sadiya Ali Rano1
1Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Nigeria
2Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, South Africa
3Department of Mathematics and Statistics, Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon (RMUTP), Bangkok, Thailand
4Department of Mathematics, Faculty of Science, KMUTT Fixed Point Research Laboratory, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand
5Department of Mathematics, Faculty of Science, Usmanu Danfodio University, Sokoto, Nigeria

Tóm tắt

Bài báo này tập trung vào vấn đề các phương trình phi tuyến có ràng buộc lồi liên quan đến các toán tử đồng monotone trong không gian Euclid. Một phương pháp gradient đồng điều kiện loại Fletcher và Reeves không dựa vào đạo hàm được đề xuất. Phương pháp đề xuất này được thiết kế để đảm bảo tính chất giảm dần của hướng tìm kiếm ở mỗi lần lặp. Hơn nữa, sự hội tụ của phương pháp đề xuất được chứng minh dưới giả định rằng toán tử nền tảng là đồng monotone và liên tục Lipschitz. Các kết quả số liệu cho thấy phương pháp này hiệu quả đối với các bài toán kiểm tra đã cho.

Từ khóa

#phương trình phi tuyến #toán tử monotone #phương pháp gradient không dựa vào đạo hàm #hội tụ #liên tục Lipschitz

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