随机互补问题及其在交通均衡中的应用

As a special case of finite variational inequality, complementarity problem has extensive applications in supply chain problem, traffic equilibrium problem, and many other areas. Since some elements may involve uncertain data in practice, stochastic variational inequality problem (SVIP) and stochastic complementarity problem (SCP) has drawn lots of attentions of researchers recently. We will employ the NCP function for complementarity theory to define a loss function in portfolio optimization and use conditional value-at-risk in risk measure, to present a reasonable deterministic model for solving SCP. About this model, we will establish corresponding optimality theory. Further, we will develop effective algorithms for solving SCP and establish convergence analysis. Moreover, the traffic problems draw attentions of government more and more recently. One reason is lack of overall strategy and planning of traffic scientifically in present traffic problems. So studying the traffic equilibrium problem has great practical significance and the research results will also provide theoretical basis to ease traffic problems. This item will employ SCP, what is a new tool to research traffic equilibrium problem which involved stochastic factors and establish complementary model of traffic equilibrium problem, which has more extensive application. After that, we will use above theory of SCP to develop corresponding effective algorithms and give examples combined with practical application.

互补问题作为有限维变分不等式的一种特殊情形在供应链问题、交通均衡问题等方面都有着广泛的应用。由于实际问题具有许多不确定因素，近年来随机变分不等式（SVIP）和互补问题（SCP）引起了众多学者的重视。本项目将利用互补理论中的NCP函数来构造投资组合优化中的损失函数，并应用风险测度理论中的条件风险值给出求解SCP的合理的确定性模型。关于这个模型，我们将建立相应的最优性理论，进而开发出求解SCP的更为有效的算法并建立收敛性分析。此外，近年来交通问题已日益引发政府的重视。当前的交通问题中，一个重要原因是，缺乏科学的整体交通战略和规划。因此研究交通均衡问题具有十分重要的实际意义，其研究成果也将为缓解交通问题提供理论依据。本项目将以SCP这一新工具来研究含有随机因素的交通均衡问题，建立应用更为广泛的交通均衡问题的互补模型。然后利用以上SCP理论研究相应的有效算法并结合实际应用给出算例。

互补问题作为有限维变分不等式的一种特殊情形在供应链问题、交通均衡问题等方面都有着广泛的应用。由于实际问题具有许多不确定因素，例如：天气、喜好、需求等。为此，本项目研究了含有随机因素的随机互补问题（SCP）。本项目利用互补理论中的NCP函数来构造投资组合优化中的损失函数，并应用风险测度理论中的条件风险值给出求解SCP的合理的确定性模型。关于这个模型，我们建立了相应的最优性理论，并开发出求解SCP的更为有效的算法，建立了收敛性分析。此外，本项目还研究了一类特殊的随机互补问题，给出了其期望残差最小化模型的一些性质。在应用方面，本项目以SCP这一新工具来研究含有随机因素的交通均衡问题，建立了应用更为广泛的交通均衡问题的随机互补模型。然后利用所得关于SCP的理论，给出求解模型的有效算法，并结合实际应用给出算例。