应365bet邀请，南京大学数学系杨俊峰博士2014.11.27--2014.12.1访问我校进行科研合作交流活动。

        报告题目： A general inertial proximal point method for mixed variational inequality problem
        报告时间：2014年11月30日（星期日）下午4:00           
        报告地点：理科楼202
                       
        Abstract:
In this paper, we first propose a general inertial proximal point method for the mixed variational inequality (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for   inertial type proximal point methods. Under certain conditions, we are able to establish the global convergence and a $o(1/k)$ convergence rate result (under certain measure) of the proposed general inertial proximal point method. We then show that both the linearized augmented Lagrangian method (ALM) and the linearized alternating direction method of multipliers (ADMM) for structured convex optimization are applications of a general proximal point method, provided that the algorithmic parameters are properly chosen. As byproducts of this finding, we establish global convergence and $O(1/k)$ convergence rate results of the linearized ALM and  ADMM  in both ergodic and nonergodic sense. In particular, by applying the proposed inertial proximal point method for mixed VI to structured convex optimization, we obtain inertial versions of the linearized ALM and ADMM whose global convergence are guaranteed. We also demonstrate the effect of the inertial extrapolation step via experimental results on the compressive principal component pursuit problem.
 

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