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数学研究院学术报告：Two-Stage Quadratic Games under Uncertainty and their Solution by Progressive Hedging Algorithms
报告时间：2019年9月23日（周一） 16：00-17：00
报告地点：西教五416
报告题目：Two-Stage Quadratic Games under Uncertainty and their Solution by Progressive Hedging Algorithms
报告嘉宾：张敏 副研究员（中国科学院新疆生态与地理研究所）
报告摘要：
A model of a two-stage N-person noncooperative game under uncertainty is studied, in which at the first stage each player solves a quadratic program parameterized by other players' decisions and then at the second stage 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. The problem of finding a Nash equilibrium of this game is shown to be equivalent to a stochastic linear complementarity problem. A linearly convergent progressive hedging algorithm is proposed for finding a Nash equilibrium if the resulting complementarity problem is monotone. For the nonmonotone case, it is shown that, as long as the complementarity problem satisfies an additional elicitability condition, the progressive hedging algorithm can be modified to find a local Nash equilibrium at a linear rate. The elicitability condition is reminiscent of the sufficient second-order optimality condition in nonlinear programming. Various numerical experiments indicate that the progressive hedging algorithms are efficient for mid-sized problems. In particular, the numerical results include a comparison with the best response method that is commonly adopted in the literature.
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报告嘉宾介绍：
张敏，副研究员，于2018年底入选中国科学院百人计划C类，在中国科学院新疆生态与地理研究所工作。本、硕、博均毕业于天津大学，本科专业为数学与应用数学专业，并辅修了计算机科学与技术专业双学位，于2010年获得理学学士与工学学士学位。2010-2016年在天津大学数学系运筹学与控制论专业硕博连读，并于2014年获得国家基金委资助，以联合培养博士生的身份公派赴澳大利亚科廷大学进行为期一年的学习。2016年6月于天津大学获得博士学位，同年8月至2019年6月在澳大利亚科廷大学跟随国际著名的优化专家孙捷教授做博士后，主要研究方向为随机变分不等式、逐步对冲算法和稀疏优化，曾参与国家自然科学基金项目3项，在SIAM Journal of Optimization, IEEE Transaction on Information Theory, Applied Mathematics and Computation等SCI期刊上发表论文12篇。
