Computational Methods for Equilibrium Problems with Micro-Level Data

微观数据平衡问题的计算方法

• 批准号: 0106880
• 负责人: Steven Gabriel
• 金额: $ 23.91万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-15 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0106880&HistoricalAwards=false
• 关键词: Computational; Methods; Equilibrium; Problems; Micro

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.

这项工作的目的是检查系统的微观层面的数据，某种平衡是要达到的。 一个重要的例子是天然气系统分析模型（GSAM），这是一个模块化的、基于数据库的北美天然气系统模型，是为美国开发的。S.能源部。 GSAM是一个大规模的非线性程序，根据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。 与供应曲线以封闭形式已知的经典方法不同，GSAM使用17，000多个天然气储层的数据库从“自下而上”建立供应曲线，同时考虑到这些曲线的跨区域和跨时间的相互依赖性。 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给曲线，它使均衡计算变得更加困难。 拟议的工作有两个主要目标。 首先，通过使用变分不等式问题（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解决GSAM类型的问题，利用特定的问题结构。 迭代方法从优化和方程求解是用来开发适当的算法为这个task.Due最近的信息技术的进步，它现在是可能的，在相当复杂的系统中的单个代理的活动建模。 在科学和工程环境中使用微观数据的应用实例比比皆是。 虽然这些系统的模拟可以使用例如复杂的“如果-那么”类型的规则而相当精细，但是以严格的方式确定系统的平衡行为可能是具有挑战性的。 部分困难是由于缺乏封闭形式的表达式来描述系统。 拟议的工作将检查一个这样的系统在其一般形式和发展的理论平衡以及有效的数学算法来计算这样的解决方案。 这项工作的预期影响是极大地推进了解决大规模均衡问题的最新技术，这些问题使用微观层面的数据来建模个体代理的经济行为。 这是重要的，因为现在许多类似的系统建模，不包含封闭形式的表达式的关键元素，但平衡的解决方案是可取的。