Distributionally Robust Optimization with Matrix Moment Constraints: Lagrange Duality and Cutting Plane Methods
讲座名称：
Distributionally Robust Optimization with Matrix Moment Constraints: Lagrange Duality and Cutting Plane Methods
讲座时间：
2016-07-12
讲座人：
徐慧福
形式：
校区：
兴庆校区
实践学分：
讲座内容：
应数学与统计学院邀请，国际著名优化专家，英国南安普顿大学运筹学教授徐慧福（Huifu Xu）博士将于2016年7月10日到2016年7月21日访问我校，并做如下学术讲座。
报告题目：Distributionally Robust Optimization with Matrix Moment Constraints: Lagrange Duality and Cutting Plane Methods
报告时间：2016年7月12日，10:10—12:00
报告地点：理科楼407
讲座内容：A key step in solving minimax distributionally robust optimization (DRO) problems is to reformulate the inner maximization w.r.t. probability measure as a semi-infinite programming problem through Lagrange dual. Slater type conditions have been widely used for zero dual gap when the ambiguity set is defined through moments. In this paper, we investigate effective ways for verifying the Slater type conditions and introduce other conditions which are based on lower semi-continuity of the optimal value function of the inner maximization problem. Moreover, we apply a random discretization scheme to approximate the semi-infinite constraints of the dual problem and demonstrate equivalence of the approach to random discretization of the ambiguity set. Two cutting plane schemes are consequently proposed: one for the discretized dualized DRO and the other for the minimax DRO with discretized ambiguity set. Convergence analysis is presented for the approximation schemes in terms of the optimal value, optimal solutions and stationary points. Numerical results are reported for the resulting algorithms.
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