A Novel Class of Iteration Algorithm for Solving Constrained Tikhonov Regularization

Speaker:     Prof. Ning Zheng

Time:          Jun.11.2021 15:00-16:00

Location:    SIST 2-400

Host:            Prof. Yue Qiu

Abstract：

The solution of discrete ill-posed problems arises in many areas of science and engineering. Instead of solving the original problem, a regularized problem whose solution is less sensitive to the error in the data is considered. The regularized problem contains a fidelity term and a regularization term, and the balance between these terms is determined by a regularization parameter. In many applications, such as in image restoration, the desired solution is known to live in a convex set, such as the nonnegative orthant. It is natural to require the computed solution of the regularized problem to satisfy the same constraints. We propose a general modulus based iterative method for computing a constrained approximate solution with Golub-Kahan bidiagonalization. Convergence of the iterative method is shown, and numerical examples that illustrate the performance of the proposed method are presented.

Bio：

郑宁博士，同济大学数学科学学院助理教授。同济大学应用数学本科，获同济大学数学系理学博士学位和日本综合研究大学院大学信息学博士学位，获上海市优秀博士毕业生和日本国立信息学研究所最佳研究工作等荣誉称号。曾在日本国立信息学研究所和日本理化学研究所担任特别研究员职务。主要从事约束不适定反问题快速算法和美式期权定价数值方法研究，在SIAM，NLAA，JSC等杂志上发表多篇学术论文。

SIST Seminar 202114