论文标题
与整数变量的双层随机线性编程中存在解决方案
Existence of Solutions in Bi-level Stochastic Linear Programming with Integer Variables
论文作者
论文摘要
已知在BI级线性程序中添加较低级别的积分约束会导致明显较弱的分析性能。最值得注意的是，乐观设置中的上层目标函数缺乏较低的半持续性，并且在标准假设下不能保证最佳解决方案的存在。在本文中，我们研究了一个环境，其中较低级别约束系统的右侧受领导者的选择以及实现某些随机向量的影响。假设只有追随者在完整信息下决定，我们采用凸风险措施来评估上层结果。将分析局限于较低级别可行集合是有限的情况下，我们为领导者风险功能的Hölder连续性提供了足够的条件，并得出了有关最佳解决方案存在的结论。最后，我们研究了基本概率措施的扰动的定性稳定性。考虑到弱收敛的拓扑，我们证明了目标函数与领导者的决策和潜在概率措施的关节连续性。
The addition of lower level integrality constraints to a bi-level linear program is known to result in significantly weaker analytical properties. Most notably, the upper level goal function in the optimistic setting lacks lower semicontinuity and the existence of an optimal solution cannot be guaranteed under standard assumptions. In this paper, we study a setting where the right-hand side of the lower level constraint system is affected by the leader's choice as well as the realization of some random vector. Assuming that only the follower decides under complete information, we employ a convex risk measure to assess the upper level outcome. Confining the analysis to the cases where the lower level feasible set is finite, we provide sufficient conditions for Hölder continuity of the leader's risk functional and draw conclusions about the existence of optimal solutions. Finally, we examine qualitative stability with respect to perturbations of the underlying probability measure. Considering the topology of weak convergence, we prove joint continuity of the objective function with respect to both the leader's decision and the underlying probability measure.
