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Số người truy cập: 75,088,890

 Sparsity regularization of the diffusion coefficient identification problem: well-posedness and convergence rates
Tác giả hoặc Nhóm tác giả: Pham Quy Muoi
Nơi đăng: Bulletin of the Malaysian Mathematical Sciences Society; Số: 39(3);Từ->đến trang: 1145-1164;Năm: 2016
Lĩnh vực: Tự nhiên; Loại: Bài báo khoa học; Thể loại: Quốc tế
TÓM TẮT
In this paper, we investigate sparsity regularization for the diffusion coefficient identification problem. Here, the regularization method is incorporated with the energy functional approach. The advantages of our approach are to deal with convex minimization problems. Therefore, the well-posedness of the problem is obtained without requiring regularity property of the parameter. The convexity of regularized problems also allows to use the fast algorithms developed recently. Furthermore, the convergence rates of the method are obtained under a simple source condition.
The main results of the paper are the well-posedness and convergence rates of sparsity regularization. We also obtain some new results of the continuity and the differentiability of related operators.
ABSTRACT
In this paper, we investigate sparsity regularization for the diffusion coefficient identification problem. Here, the regularization method is incorporated with the energy functional approach. The advantages of our approach are to deal with convex minimization problems. Therefore, the well-posedness of the problem is obtained without requiring regularity property of the parameter. The convexity of regularized problems also allows to use the fast algorithms developed recently. Furthermore, the convergence rates of the method are obtained under a simple source condition.
The main results of the paper are the well-posedness and convergence rates of sparsity regularization. We also obtain some new results of the continuity and the differentiability of related operators.
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