This paper studies the stochastic programming problem with a quantile criterion in the classical single-stage statement under the assumption that the loss function is linear in random parameters. An extension of this problem is the minimax one in which the inner maximum of the loss function is taken with respect to the realizations of the vector of random parameters over the kernel of its probability distribution, and the outer minimum is taken with respect to the optimized strategy over a given set of admissible strategies. The extension principle of optimization problems is used to establish the following result: under a sufficient condition in the form of a certain probabilistic constraint, the optimal solution of this minimax problem is also optimal in the original problem with the quantile criterion.

假设损失函数在随机参数中是线性的，本文采用分位数准则研究经典单阶段语句中的随机规划问题。这个问题的扩展是极小极大，其中损失函数的内极大是关于随机参数向量在其概率分布的核上的实现的，而极小是关于优化的概率的。给定的一组可接受策略上的策略。使用优化问题的扩展原理来建立以下结果：在具有一定概率约束形式的充分条件下，该极小极大问题的最优解在具有分位数标准的原始问题中也是最优的。