论文标题
解决方案集的概率可行性保证了不确定的变异不平等
Probabilistic feasibility guarantees for solution sets to uncertain variational inequalities
论文作者
论文摘要
我们开发了一种数据驱动的方法来计算A型可行性证书，以对受不确定性影响的变异不平等的解决方案集进行计算。具体而言，我们专注于具有确定性映射和不确定性设置的变异不平等现象，并通过场景表示不确定性。在方案方法文献中最新进展的基础上，我们量化了各种不平等的整个解决方案集合的鲁棒性特性，并使用场景方法构建了可行性集，并与不确定性的新的未见认识。我们的结果扩展了现有的结果，通常会假设解决方案集是单胎，并且需要某些非分类属性，从而为任何可行解决方案提供了概率可行性的保证。我们表明，评估一组解决方案的违规概率，而不是单胎的违规概率，需要列举“塑造”该集合的支持约束。此外，我们提出了一个一般过程，以列举不需要封闭形式的解决方案集的支持约束，这不太可能可用。我们表明，强大的游戏理论问题可以通过不确定的变异不平等进行建模，并通过对涉及电动汽车充电协调问题的案例研究进行大量数值模拟来说明我们的理论结果。
We develop a data-driven approach to the computation of a-posteriori feasibility certificates to the solution sets of variational inequalities affected by uncertainty. Specifically, we focus on instances of variational inequalities with a deterministic mapping and an uncertain feasibility set, and represent uncertainty by means of scenarios. Building upon recent advances in the scenario approach literature, we quantify the robustness properties of the entire set of solutions of a variational inequality, with feasibility set constructed using the scenario approach, against a new unseen realization of the uncertainty. Our results extend existing results that typically impose an assumption that the solution set is a singleton and require certain non-degeneracy properties, and thereby offer probabilistic feasibility guarantees to any feasible solution. We show that assessing the violation probability of an entire set of solutions, rather than of a singleton, requires enumeration of the support constraints that "shape" this set. Additionally, we propose a general procedure to enumerate the support constraints that does not require a closed form description of the solution set, which is unlikely to be available. We show that robust game theory problems can be modelling via uncertain variational inequalities, and illustrate our theoretical results through extensive numerical simulations on a case study involving an electric vehicle charging coordination problem.
