The error and perturbation bounds for the absolute value equations with their applications in the horizontal linear complementarity problem

吴世良

时间：2023-02-10    09：00-10：00  (周五上午)  

地点: 沙河主E座-404   腾讯会议 ID：733-673-794    

摘要:  In this talk, by introducing a class of absolute value functions, we study the error bounds and perturbation bounds for two types of absolute value equations (AVEs): $Ax-B|x|=b$ and $Ax-|Bx|=b$. Some useful error bounds and perturbation bounds for the above two types of absolute value equations are presented. By applying the absolute value equations, we obtain some useful error bounds and perturbation bounds for the horizontal linear complementarity problem (HLCP). Incidentally, two new  error bounds for linear complementarity problem (LCP) are given, coincidentally, which are equal to the existing result. Without constraint conditions, a new perturbation bound for the LCP is given as well. Besides, without limiting the matrix type, some computable estimates for the above upper bounds are given, which are sharper than some existing results under certain conditions. Some numerical examples for the AVEs from the LCP are given to show the feasibility of the perturbation bounds.

报告人简介: 吴世良，博士，教授，硕士生导师。2020.02至今任职于云南师范大学数学学院。研究方向为数值代数、最优化的理论与方法，研究兴趣包括绝对值方程组，互补问题等。

邀请人：韩德仁

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