报告题目：A Diagonal BFGS method

报告人：李董辉（华南师范大学）

时间：2016-05-14

地点：数学与统计学院一楼报告厅

摘要： Quasi-Newton method is one of the most important class of algorithms for unconstrained Optimization. The quasi-Newton matrices produced by standard Quasi-Newton method are generally dense. Thus these methods are not able to solve large-scale problems. Sparse quasi-Newton method can be applied to solve large-scale optimization problems. The sparsity of these the quasi-Newton matrices in the existing sparse quasi-Newton methods rely on the sparsity of the Hessian of the objective function. In this thesis, we propose a diagonal type BFGS method which has the advantages that the sparsity of the quasi-Newton matrix is independent of the sparsity of the Hessian of the objective function. Moreover, the generated quasi-Newton matrices are positive definite. As a consequently, the method is a decent method. Under appropriate conditions, we prove that the diagonal BFGS method with Wolfe line search is globally convergent. Numerical results show that even without a line search progress, the method is numerically efficient.

报告时间：5月14日下午4点

报告人简介：

李董辉，现任华南师范大学教授、博士生导师，优化领域的著名学者，中国运筹学会常务理事。1994年获湖南大学理学博士学位，1999年获日本京都大学工学博士学位。先后访问日本京都大学、澳大利亚新南威尔士大学、香港理工大学、香港城市大学。现任《Pacific Journal of Optimization》、《系统工程理论与实践》等SCI和EI杂志的编委。主持多项国家自然科学基金和教育部重大项目。李教授的主要研究方向有：最优化理论与算法、非线性方程组的数值解法、投资组合最优化、物流与供应链管理。李教授在《SIAM J. Numer. Anal.》、《SIAM J. Optim.》、《Math. Comput.》、《Numer. Math.》等相关领域的顶级期刊上发表论文50多篇。其关于拟牛顿方法求解非凸优化问题和非线性方程组的全局收敛性的系列论文已成为该领域的经典文献，受到国内外同行的高度评价和广泛引用。