報告時間：2019年9月23日(周一) 16:00-17:00
報告地點：北辰校區(qū)西教五416
報告題目：Two-Stage Quadratic Games under Uncertainty and their Solution by Progressive Hedging Algorithms
報告嘉賓：張敏 副研究員（中國科學院新疆生態(tài)與地理研究所）
報告摘要：
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.
.
嘉賓介紹：
張敏，副研究員，于2018年底入選中國科學院百人計劃C類，在中國科學院新疆生態(tài)與地理研究所工作。本、碩、博均畢業(yè)于天津大學，本科專業(yè)為數(shù)學與應用數(shù)學專業(yè)，并輔修了計算機科學與技術專業(yè)雙學位，于2010年獲得理學學士與工學學士學位。2010-2016年在天津大學數(shù)學系運籌學與控制論專業(yè)碩博連讀，并于2014年獲得國家基金委資助，以聯(lián)合培養(yǎng)博士生的身份公派赴澳大利亞科廷大學進行為期一年的學習。2016年6月于天津大學獲得博士學位，同年8月至2019年6月在澳大利亞科廷大學跟隨國際著名的優(yōu)化專家孫捷教授做博士后，主要研究方向為隨機變分不等式、逐步對沖算法和稀疏優(yōu)化，曾參與國家自然科學基金項目3項，在SIAM Journal of Optimization, IEEE Transaction on Information Theory, Applied Mathematics and Computation等SCI期刊上發(fā)表論文12篇。
