分布鲁棒最小二乘问题的割平面算法

Cutting plane method for distributionally robust least squares problems

实际应用中很多重要问题可以转化为最小二乘问题.提出一种在一般最小二乘问题中用数据的概率不确定性描述的鲁棒框架,它的不确定分布集是通过测度有界的矩约束给出的.此时,它为一个凸优化问题.当样本空间具有有限支撑时,可以用割平面算法在有限步求解,而算法可以通过线性规划和线性锥规划相关的求解器来实现.

Many important problems in the practical application can be converted to the least squares problem.We present the robust framework using probabilitic ambiguity descriptions of the date in least squares problems,the ambiguity distribution set is given by bounds on the probability measure with moments constraints.At this time,it is a convex optimization problem.It can be solved using the cutting plane methodin finite steps when the sample space has finite support.This method can be achieved by the solver which is related to linear programming and linear cone programming.