学术报告

报告题目: Maximizing Perturbation Radii for Robust Convex Quadratically Constrained Quadratic Programs

报告人：邢文训（清华大学 教授 博导）

报告时间：2021年11月26日 15：00—16：30

报告地点：腾讯会议 (ID: 690 239 911)

主办单位: 数学与统计学院

摘要: Under the assumption that uncertain coefficients corresponding to each constraint are perturbed in an ellipsoidal set, we consider the problem of maximizing the perturbation radius of the ellipsoidal set associated to a robust convex quadratically constrained quadratic programming problem to maintain some properties of a pre-decision. To this end, a fractional programming problem is first formulated to solve the problem, and then equivalently reformulated into linear conic programs over positive semi-definite, second-order cones that are solvable in polynomial time. Numerical experiments in connection with the robust Markowitz's portfolio selection problem are provided to demonstrate the proposed concept of sensitivity analysis. Additionally, certain numerical results are also presented to compare the efficiency of direct solutions of the proposed linear conic programs with that of a bisection method for the corresponding fractional programming problem.

简介: 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。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）。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7部，主持国家级项目多项，兼任中国运筹学会监事，数学规划分会常务理事，JIMO，JORSC编委等。