论文标题
带有随机的第二阶段成本向量的两阶段混合成员求助模型的凸近近似的参数误差界限
Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector
论文作者
论文摘要
我们考虑了两个阶段的追索模型，其中第二阶段问题在第二阶段成本向量，技术矩阵和右侧向量中具有整数决策变量和不确定性。这种混合辅助模型通常是非凸的，因此很难解决。这些模型的凸近似值具有随附的误差界限。但是，尚不清楚这些错误界限如何取决于第二阶段成本向量$ q $的分布。实际上，唯一已知的错误链接取决于$ q $具有有限支持的假设。在本文中，我们得出参数错误界限，其依赖于$ q $的分布是明确的，并且对于任何分布$ q $的分布而言，只要它具有有限的预期$ \ ell_1 $ -norm。我们发现，错误在$ \ el_1 $ norm $ q $的预期值中线性界限。
We consider two-stage recourse models in which the second-stage problem has integer decision variables and uncertainty in the second-stage cost vector, technology matrix, and the right-hand side vector. Such mixed-integer recourse models are typically non-convex and thus hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector $q$. In fact, the only error bound that is known hinges on the assumption that $q$ has a finite support. In this paper, we derive parametric error bounds whose dependence on the distribution of $q$ is explicit and that hold for any distribution of $q$, provided it has a finite expected $\ell_1$-norm. We find that the error bounds scale linearly in the expected value of the $\ell_1$-norm of $q$.
