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Về Chỉ Số Tốpô của Giải Pháp cho Bất Đẳng Thức Biến Thiên Trên Các Manifol Riemann
Tóm tắt
Trong bài báo này, dựa trên lý thuyết chỉ số điểm cố định cho một lớp các bản đồ đa giá trị \(\widetilde{J}\) trên các diện tích lân cận tuyệt đối, chúng tôi giới thiệu khái niệm về chỉ số khả thi cho một bất đẳng thức biến thiên trên một manifold Riemann liên quan đến một trường vectơ đa giá trị. Chúng tôi mô tả các tính chất chính của đặc trưng tốpô này và sử dụng nó để biện minh cho sự tồn tại của một giải pháp cho bài toán bất đẳng thức biến thiên. Như một ứng dụng, bài toán tối ưu hóa một hàm chức không trơn trên một manifold Hadamard được xem xét.
Từ khóa
#bất đẳng thức biến thiên #manifold Riemann #chỉ số tốpô #trường vectơ đa giá trị #tối ưu hóa hàm chức không trơnTài liệu tham khảo
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