學術報告:Two-Stage Quadratic Games under Uncertainty and their Solution by Progressive Hedging Algorithms

報告時間:2019年9月23日(周一) 16:00-17:00


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與地理研究所)



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.



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與地理研究所工作。本、碩、博均畢業于天津大學缅甸真人百家le,本科專業為數學與應用數學專業,并輔修了計算機科學與技術專業雙學位,于2010年獲得理學學士與工學學士學位。2010-2016年在天津大學數學系運籌學與控制論專業碩博連讀缅甸真人百家le,并于2014年獲得國家基金委資助,以聯合培養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。20166月于天津大學獲得博士學位缅甸真人百家le,同年8月至20196月在澳大利亞科廷大學跟隨國際著名的優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缅甸真人百家le、逐步對沖算法和稀疏優化,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 ComputationSCI期刊上發表論文12篇。

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