Computational Methods for Equilibrium Problems with Micro-Level Data

这项工作的目标是检查具有微观数据的系统，对于这些系统，将达到某种类型的平衡。一个重要的例子是天然气系统分析模型(GSAM)，这是为美国能源部开发的北美天然气系统的模块化、基于储气库的模型。在目前的形式下，GSAM是一个大规模的非线性程序，基于最大化总剩余减去运输成本的概念计算市场均衡价格、数量、流量和其他价值的估计。与封闭形式已知供应曲线的经典方法不同，GSAM使用17,000多个天然气储集层的数据库，从“自下而上”建立供应曲线，同时考虑到这些曲线的区域间和跨期相互依存关系。虽然这种“自下而上”的特征提供了很好的现实性，但由于缺乏封闭形式的供应曲线，它使得均衡计算变得更加困难。拟议的工作有两个主要目标。首先，通过使用变分不等问题(VIP)和非线性互补问题(NCP)格式，注意季节性市场价格(拉格朗日乘数)与天然气需求、储存活动水平、投资决策等之间的函数关系，更一般地分析GSAM市场均衡问题。第二个主要任务是开发有效的方法来利用特定的问题结构来解决GSAM类型的问题。最优化和方程求解的迭代方法被用来开发适合这一任务的算法。由于最近的信息技术的进步，现在可以对相当复杂的系统中的单个代理的活动进行建模。在科学和工程环境中使用微观数据的应用例子比比皆是。虽然使用例如复杂的“如果-然后”类型的规则可以相当详细地模拟这些系统，但以严格的方式确定系统的均衡行为可能是具有挑战性的。困难的部分原因是缺乏描述系统的封闭形式表达式。这项拟议的工作将研究一个这样的系统的一般形式，并开发出平衡理论和有效的数学算法来计算这样的解。这项工作的预期影响是极大地提高解决大规模均衡问题的技术水平，这些问题使用微观数据来建模单个代理人的经济行为。这一点很重要，因为许多类似的系统现在都被建模，这些系统不包含关键元素的闭合形式表达式，但需要平衡解。

The objective of this work is to examine systems with micro-level data for which an equilibrium of some sort is to be reached. One important example is the Gas Systems Analysis Model (GSAM), a modular, reservoir-based model of the North American natural gas system developed for the U. S. Department of Energy. In its current form, GSAM is a large-scale nonlinear program that computes estimates of market equilibrium prices, quantities, flows, and other values based on the notion of maximizing total surplus less transportation costs. Unlike the classical approach in which supply curves are known in closed form, GSAM builds supply curves from the "bottom up" using a data base of over 17,000 natural gas reservoirs taking into account both the interregional as well as intertemporal interdependence of these curves. While this "bottom up" feature provides a good deal of realism, it renders the equilibrium computations much more difficult due to the lack of closed form supply curves. The proposed work has two main objectives. First, analyze the GSAM market equilibrium problem more generally by noting the functional relationships between seasonal market prices (Lagrange multipliers) and demand for gas, storage activity levels, investment decisions, etc. using the variational inequality problem (VIP) and nonlinear complementarity problem (NCP) formats. The second main task is to develop efficient methods to reach a solution to GSAM-type problems exploiting the particular problem structure. Iterative methods from optimization and equation solving is used to develop appropriate algorithms for this task.Due to recent advances in information technology, it is now possible to model the activities of individual agents in rather complicated systems. Examples of applications in scientific and engineering settings using micro-level data abound. While simulations of these systems can be rather elaborate using for example, complicated "if-then" type rules, determining equilibrium behavior of the system in a rigorous manner can be challenging. Part of the difficulty is due to a lack of closed form expressions for describing the system. The proposed work will examine one such system in its general form and develop both a theory for equilibrium as well as efficient mathematical algorithms to compute such a solution. The anticipated impact of this work is to greatly advance the state of the art in solving large-scale equilibrium problems that use micro-level data for modeling the economic behavior of individual agents. This is significant since many similar systems are now modeled that contain no closed form expressions for key elements but for which an equilibrium solution is desirable.