主办单位：数学与财经学院

主 讲 人：叶明露

主讲人简介：

叶明露，西华师范大学副教授，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。

讲座一：A half space projection method for solving generalized Nash equilibrium problems

讲座时间：2019年4月1日（周一）14:30-16:00

讲座地点：知津楼C303

内容简介：

The generalized Nash equilibrium problem (GNEP) is an n-person noncooperative game in which each players strategy set depends on the rival's strategy set. In this paper, we presented a hyperplane projection method for solving the quasi-variational inequalitiy problem (QVIP) which is a formulation of the GNEP. This method is simple and admits a nice geometric interpretation. It consists of two steps. First, a half-space which can separate strictly the current point with the \strong solution" of QVIP is obtained. Then the next iterate point is obtained by projecting the current iterate point onto this speci_c half-space. Thus, the next iterate point can be represented explicitly. The global convergence is proved under the minimal assumptions. We also present some numerical results to illustrate the feasibility of our method, which show that our method not only outperforms the projection-like methods of Zhang et al. (2010) but also more stable than the method of Han etal. (2012).

讲座二：A subgradient-based approach for finding the maximum feasible subsystem with respect to a set

讲座时间：2019年4月2日（周二）14:30-16:00

讲座地点：知津楼C303

内容简介：

We propose a subgradient-based method for finding the maximum feasible subsystem in a collection of closed sets with respect to a given closed set $C$ (MFS$_C$). In this method, we reformulate the MFS$_C$ problem as an $\ell_0$ optimization problem and construct a sequence of continuous optimization problems to approximate it. The objective of each approximation problem is the sum of the composition of a nonnegative nondecreasing continuously differentiable concave function with the squared distance function to a closed set. Although this objective function is nonsmooth in general, a subgradient can be obtained in terms of the projections onto the closed sets. Based on this observation, we adapt a subgradient projection method to solve these approximation problems. Unlike classical subgradient methods, the convergence (clustering to stationary points) of our subgradient method is guaranteed with a {\em nondiminishing stepsize} under mild assumptions. This allows us to further study the sequential convergence of the subgradient method under suitable Kurdyka-{\L}ojasiewicz assumptions.