标题： 带有畸变风险约束的随机线性规划 显示英文标题

标题： Stochastic linear programming with a distortion risk constraint

摘要： 研究了参数具有不确定性的线性优化问题。我们应用一致畸变风险度量来捕捉约束可能被违反的情况。每个风险约束都会诱导出一个系数的不确定性集，该集被证明是一个加权均值截断区域。给定系数的一个外部样本，不确定性集是一个可以精确计算的凸多面体。我们构建了一个有效的几何算法来求解具有单一畸变风险约束的随机线性规划问题。该算法作为一个R包可用。此外，当样本独立同分布时，还研究了该算法的渐近行为。最后，我们展示了一些计算经验。 显示英文摘要

摘要： Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients, which is shown to be a weighted-mean trimmed region. Given an external sample of the coefficients, an uncertainty set is a convex polytope that can be exactly calculated. We construct an efficient geometrical algorithm to solve stochastic linear programs that have a single distortion risk constraint. The algorithm is available as an R-package. Also the algorithm's asymptotic behavior is investigated, when the sample is i.i.d. from a general probability distribution. Finally, we present some computational experience.