关于举行杭州电子科技大学凌晨教授学术报告会的通知

报告题目：A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with M-tensors

报  告 人：凌晨 教授 （杭州电子科技大学）

报告时间：2019年11月22日（星期五 ）上午9:45-10:30             

报告地点：4号楼 4318 室

邀 请 人：潘少华 教授

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数学学院

2019年11月11日

报告摘要：

We consider multilinear systems of equations whose coefficient tensors are Mtensors. Multilinear systems of equations have many applications in engineering and scientific computing, such as data mining and numerical partial differential equations. In this talk, we show that solving multilinear systems with M-tensors is equivalent to solving nonlinear systems of equations where the involving functions are P-functions. Based on this result, we propose a Newton-type method to solve multilinear systems withM-tensors. For a multilinear system with a nonsingular M-tensor and a positive right side vector, we prove that the sequence generated by the proposed method converges to the unique solution of the multilinear system and the convergence rate is quadratic. Numerical results are reported to show that the proposed method is promising.

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报告人简介：

凌晨，杭州电子科技大学理学院教授，博士生导师。现任中国运筹学会理事、中国运筹学会数学规划分会副理事长、中国经济数学与管理数学研究会副理事长、浙江省数学会常务理事、国际ESI期刊 Pacific Journal of Optimization编委、国际期刊Statistics，Optimization & Information Computing编委，国家自然科学基金委数理科学部评审专家。研究方向：非线性规划、变分不等式与互补问题、张量计算、多变量多项式优化、半无限规划、随机规划、多目标优化理论与应用等。近十年来，主持国家自科基金和浙江省自科基金各4项、其中省基金重点项目1项。在国内外重要刊物发表论文70余篇，其中SCI期刊论文50余篇，多篇发表在Math. Program.、SIAM J. on Optim.和 SIAM J.on Matrix Anal.and Appl.、COAP、JOTA、JOGO等。