报告题目:  TWO-STAGE QUADRATIC GAMES UNDER UNCERTAINTY AND THEIR SOLUTION BY PROGRESSIVE HEDGING ALGORITHMS

报  告  人:   Sun Jie  (Curtin University/National University of Singapore)

报告时间：2018年8月17日，18:30 - 20:30

报告地点：数计学院2号楼229报告厅

报告摘要: A two-stage $N$-person non-cooperative game model under uncertainty is studied, in which each player solves a quadratic program parameterized by other players' decisions at the first stage, then the player solves a recourse quadratic program parameterized by the realization of a random vector, the second-stage decisions of other players, and the first stage decisions of all players at the second stage. The problem of finding a Nash equilibrium of this game is shown to be equivalent to a stochastic linear complementarity problem. Conditions for monotonicity of the corresponding stochastic linear complementarity problem are investigated. A progressive hedging algorithm is proposed for solving the monotone case. Various numerical experiments indicate that the progressive hedging algorithm is efficient for mid-sized monotone problems.

报告人简介:   孙捷教授是国际知名的优化专家。他在内点算法和非光滑牛顿算法有突出的贡献。目前研究兴趣集中于随机变分不等式和分布鲁棒优化问题。新加坡国立大学授予他杰出大学研究者奖并任命他为讲座教授。他1993年联名发表的一篇论文， 在2003年被评为“过去10年引用率最高的数学及统计学论文”之一。他也是国际信息科学学院评出的“2002-2012期间被引用最多”的数学家之一，曾多次受邀在国际会议上做大会演讲并应邀担任美英德日等国多种学术杂志的主编或副主编。1986-2014， 他在美国西北大学和新加坡国立大学任教。 其中1999-2008，他任新加坡-麻省理工学院联盟院士。自2014年起任澳洲科廷大学数学统计系杰出研究教授。