Randomized Kaczmarz Methods for Tensor Complementarity Problems

In this talk, we equivalently reformulate tensor complementarity problem as a system of fixed point equations. Based on this system, we propose the (extend) randomized Kaczmarz methods for solving the tensor complementarity problem (TCP) associated with nonnegative P-tensors and nonsingular M-tensors. We also analyze the upper bound of the mean squared error and the estimate of the convergence rate for these two iterative methods. The computer simulation results further substantiate that the presented two randomized Kaczmarz type method can be used to solve TCP with these two cases of tensors.

报告人简介：魏益民，复旦大学数学科学学院教授，博士生导师。担任国际学术期刊Computational and Applied Mathematics, Journal of Applied Mathematics and Computing,FILOMAT, 和 Communications in Mathematical Research, 《高校计算数学学报》的编委. 在国际学术期刊Math. Comput., SIAM J. Sci. Comput., SIAM J. Numer Anal., SIAM J. Matrix Anal. Appl., J. Sci. Comput., IEEE Trans. Auto. Control, IEEE Trans.Neural Network Learn. System, Neurocomputing 和 Neural Computation 等发表论文150余篇; 在EDP Science, Elsevier, Springer, World Scientific和科学出版社等出版英语专著5本. 5次入选爱思唯尔“中国高被引学者”榜单. Google学术引用8900余次，H 指数 48.