信息科学技术学院数学系学术讲座（十三）
题 目：Expected Residual Minimization for Stochastic Variational Inequalities
内容简介：There is a growing literature suggesting the potential use of stochastic variational inequalities in science, engineering and economics as a powerful framework to model equilibrium problems with uncertainties, data errors and/or dynamic scenarios. In the recent years, many approaches for finding different types of “here-and- now” and “wait-and-see” solutions of stochastic variational inequalities have been developed. This talk presents a new expected residual minimization formulation to find “here-and-now” solution for a class of stochastic variational inequalities. The objective function of the expected residual minimization problem is nonnegative and Lipschitz continuous. Moreover, it is convex for some stochastic linear variational inequalities, which helps us guarantee the existence of a solution and convergence of approximation methods. We propose a globally convergent (a.s.) smoothing sample average approximation (SSAA) method to minimize the expected residual function. We show that the residual minimization problem and its SSAA problems have minimizers in a compact set and any cluster point of minimizers and stationary points of the SSAA problems is a minimizer and a stationary point of the expected residual minimization problem (a.s.). Examples from traffic assignment under uncertainties show that the solutions generated by the expected residual minimization formulation with the SSAA procedure have desirable properties.
报告人：香港理工大学应用数学系系主任 陈小君 讲座教授
报告人简介：陈教授是世界著名最数值优化专家，多年以来一直从事科学计算，最优化的研究工作。尤其对线性互补问题，非光滑优化问题有突出贡献。
时 间：2014年11月2日（周日）下午4：00始
地 点：南海楼330室
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信息科学技术学院