报告人：Darinka Dentcheva教授

Stevens Institute of Technology, Hoboken, New Jersey 07030, USA

题目：Optimization Problems with Stochastic-order Constraints

时间：2018年5月30日下午16:00

地点：海韵实验楼105

摘要：Stochastic orders formalize preferences among random outcomes and are widely used in statistics and economics. We focus on stochastic optimization problems involving stochastic-order relations as constraints that relate performance operators to benchmark random outcomes with acceptable distributions. The performance operators depend on our decisions and have values in an appropriate space of random variables. Necessary and sufficient conditions of optimality and duality theory for these problems will be presented. The analysis puts additional light on relations between the expected utility theory, the dual (rank-dependent) utility theory, and the theory of coherent measures of risk. We pay a special attention to the first and second order stochastic dominance, and the increasing convex order.  These relations are defined by a continuum of compositions of convex non-smooth functions with possibly non-convex differentiable functions. Our results contribute to the theory of semi-infinite and composite optimization in vector spaces. Potential applications will be outlined。

报告人简介：Darinka Dentcheva holds a PhD and a Doctor of Sciences (Habilitation) degree from Humboldt University Berlin, Germany. Her current research interests are in the area of optimization under uncertainty and risk, in which she has co-authored a popular recent monograph and multiple influential papers. She is passionate about education and has developed a new graduate curriculum and lectures in the area of stochastic systems and optimization. Darinka Dentcheva is an Associate Editor of SIAM Review, the Journal on Control, Optimization and Calculus of Variations of the French Society of Applied Mathematics (ESAIM), and Frontiers in Applied Mathematics. She is a past member of the Publications Committee of the Mathematical Optimization Society and the Committee on Stochastic Programming of the Mathematical Optimization Society, and a member of the program committee of many international conferences. She is the recipient of a Deutche Academische Austausch Dienst award, Davis Memorial Research Award, and Research Recognition Award of the board of trustees of Stevens Institute of Technology.

联系人:教授、林建华助理教授

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