报告一题目：测地流的遍历性和部分双曲动力系统的非稠密轨道

报告人：吴伟胜

地点：信息楼343研讨室

时间：2016年4月6日（周三）下午14:00-15:00

摘要：非正曲率曲面上测地流关于Liouville测度的遍历性是一个著名的公开猜想，我们介绍如何在给定条件下来证明这个猜想。在报告的第二部分，我们讨论任意部分双曲微分同胚下的非稠密轨道，主要结果是那些具有非稠密轨道的初始点形成的集合具有满Hausdorff维数。

报告二题目：Feasible Method for Semi-Infinite Programs

报告人：王树雄

地点：信息楼343研讨室

时间：2016年4月6日（周三）下午15:00-16:00

摘要：A new numerical method is presented for semi-infinite optimization problems which guarantees that each iterate is feasible for the original problem. The basic idea is to construct concave relaxations of the lower level problem, to compute the optimal values of the relaxation problems explicitly, and to solve the resulting approximate problems with finitely many constraints. The

concave relaxations are constructed by replacing the objective function of the lower level problem by its concave upper bound functions. Under mild conditions, we prove that every accumulation point of the solutions of the approximate problems is an optimal solution of the original problem. An adaptive subdivision algorithm is proposed to solve semi-infinite optimization problems. It is shown that the Karush–Kuhn–Tucker points of the approximate problems converge to a Karush–Kuhn–Tucker point of the original problem within arbitrarily given tolerances. Numerical experiments show that our

algorithm is much faster than the existing adaptive convexification algorithm in computation time.

 

 

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