北京科学与工程计算研究院学术报告之九十一

报告人/Speaker:邢文训(清华大学数学科学系)

报告题目/Title: Fast computation of global solutions to the single-period unit commitment problem for electricity market applications

时间/Date & Time:2018年12月3日,15:30—16:30

地点/Location:理科楼M843

报告摘要/Abstract:

The single-period unit commitment problem arises from electricity markets. An efficient global algorithm not only provides the optimal schedule that achieves the lowest cost, but also plays an important role for deriving the market-clearing price. As of today, the problem is mainly solved by using a general-purpose mixed-integer quadratic programming solver such as CPLEX or Gurobi. This paper proposes an extremely efficient global optimization algorithm for solving the problem. We propose a conjugate function based convex relaxation and design a special dual algorithm to compute a tight lower bound of the problem in O(nlogn) complexity. Then, a branch-and-bound algorithm is designed for finding a global solution to the problem. Computational experiments show that the proposed algorithm solves test instances with 500 integer variables in less than 0.01 seconds, whereas current state-of-the-art solvers fail to solve the same test instances in one hour. This superior performance of the proposed algorithm clearly indicates its potential in day-ahead and real-time electricity markets.

报告人简介/About the speaker:

邢文训,清华大学数学科学系教授、博士生导师,北京大学理学学士,清华大学理学博士。目前研究兴趣为非凸/非光滑全局最优化及组合最优化问题,在国内外学术刊物SIAM Journal on Optimization, European Journal of Operational Research, IIE Transactions, Discrete Applied Mathematics, Annals of Operations Research等发表论文60余篇,出版专著1部,教材6部。2007年获得国防科工委国防科学技术进步奖(一等),2008年获国家科学技术进步奖(二等),2001年获中国运筹学会运筹学应用奖(二等)。先后主持过国家基金委面上和教育部重点课题,承担国防973二级课题负责人,及参加国家、部委及企业科研项目10余项。目前为中国运筹学会常务理事,中国运筹学会数学规划分会副主任,Journal of Industrial and Management Optimization副主编,Journal of the Operations Research Society of China编委等。


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报告人/Speaker:张立平(清华大学数学科学系)

报告题目/Title:A mixed integer programming approach to the tensor complementarity problem

时间/Date & Time:2018年12月3日,16:30—17:30

地点/Location:理科楼M843

报告摘要/Abstract:

The tensor complementarity problem is a special instance of nonlinear complementarity problems, which has many applications. How to solve the tensor complementarity problem, via analyzing the structure of the related tensor, is one of very important research issues. In this paper, we propose a mixed integer programming approach for solving the tensor complementarity problem. We reformulate the tensor complementarity problem as an equivalent mixed integer feasibility problem. Based on the reformulation, some conditions for the solution existence and some solution properties of the tensor complementarity problem are given. We also prove that the tensor complementarity problem, corresponding to a positive definite diagonal tensor, has a unique solution. Finally, numerical results are reported to indicate the efficiency of the proposed algorithm.

报告人简介/About the speaker:

张立平,清华大学数学科学系副教授,博士生导师,研究方向最优化理论算法及应用,在求解互补与变分不等式问题、半无限规划、张量优化等方面取得了一些有意义的成果。已发表高质量论文三十余篇、连续获得多项国家自然科学基金资助。曾获得教育部自然科学奖二等奖和北京市科学技术奖二等奖。