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8-30国家数学与交叉科学中心合肥分中心报告【王成】

报告题目: Preconditioned Steepest Descent (PSD) solver  for regularized convex optimization problems

报告人:王成  Associate Professor at University of Massachusetts Dartmouth

报告时间:8月30日  10:45-11:30

地点:1218

摘要:

A few preconditioned steepest descent (PSD) solvers are presented 

for the certain optimization problems, in which the solution corresponds 

to a convex energy functional. The highest and lowest order terms are 

constant-coefficient, positive linear operators. By using the 

energy dissipation property, we derive a discrete bound for 

the solution, as well as an upper-bound for the second derivative 

of the energy. These bounds allow us to investigate the 

convergence properties of our method. In particular, a geometric 

convergence rate is shown for the nonlinear PSD iteration applied 

to the regularized equation, which provides a much sharper 

theoretical result over the existing works. Some numerical 

simulation results are also presented in the talk. 

  科大主页 | 国家数学与交叉科学中心(合肥) | 中科院吴文俊数学重点实验室 |
中科院数学与系统科学研究院 | 北京国际数学研究中心 | 安徽省数学会