主 讲 人：叶明露

主办单位：数学与大数据学院

讲座时间：2020年11月3日（周二）上午9:00-10:00

讲座地点： 知津楼C303

内容简介：

It is well known that the monotonicity of the underlying mapping of variational inequalities plays a central role in the convergence analysis. In this paper, we propose an infeasible projection algorithm (IPA for short) for nonmonotone variational inequalities. The next iteration point of IPA is generated by projecting a vector onto a half-space. Hence, the computational cost of computing the next iteration point of IPA is much less than the algorithm of Ye and He (2015) (YH for short). Moreover, if the underlying mapping is Lipschitz continuous with its modulus is known, by taking suitable parameters, IPA requires only one projection onto the feasible set per iteration. The global convergence of IPA is obtained when the solution set of its dual variational inequalities is nonempty. Moreover, if in addition error bound holds, the convergence rate of IPA is Q-linear. IPA can be used for quasi-monotone variational inequalities with its dual variational inequalities is nonempty. Comparing with YH by solving high-dimensional nonmonotone variational inequalities, numerical experiments show that IPA is much more efficient than YH both from CPU time point of view and the number of iterations point of view.

主讲人简介：

西华师范大学教授，硕士研究生导师。研究方向：非线性最优化，变分不等式投影算法，非凸优化问题的算法。2014年毕业于四川师范大学数学系，获理学博士学位。2017年6月-2018年6月在香港理工大学跟随Ting Kei Pong博士后做博士后研究。2011年至今在SIAM J. Optim., Comput. Optim. Appl., Optim., J. Oper. Res. Soc. China, 应用数学学报, 数学进展等期刊发表多篇论文。部分成果削弱了经典变分不等式投影算法对单调性的假设。