Abstract

This paper employs the Dantzig-Wolfe decomposition procedure to solve large-scale economic equilibrium problems formulated as nonlinear programs with block-diagonal linear constraints, where each block characterizes the supply possibilities in a region, and a set of unifying constraints that characterize the supply-demand balances. We derive lower and upper bounds for the value of the objective function at each step of the decomposition procedure, and use the percentage deviation between the two bounds as guidance for terminating the iterations to obtain an approximation of the equilibrium solution. Our computational results with moderate-size problems show that the decomposition procedure can reduce the solution time substantially compared to the direct solution approach without using decomposition. We present a large-scale empirical application where the impacts of the US biofuel mandates on agricultural and transportation fuel sectors were analyzed. Two powerful optimization solvers could not handle the problem due to the sheer size of the model and nonlinearity involved in the objective function, whereas we could solve the economic equilibrium successfully using the decomposition approach.

摘要

本文采用 Dantzig-Wolfe 分解程序来解决大规模经济均衡问题，该问题被表述为具有块对角线性约束的非线性程序，其中每个块表征一个区域中的供应可能性，以及一组表征供应的统一约束 -需求余额。我们在分解过程的每一步推导出目标函数值的下界和上界，并使用这两个边界之间的百分比偏差作为终止迭代的指导，以获得平衡解的近似值。我们对中等规模问题的计算结果表明，与不使用分解的直接求解方法相比，分解过程可以大大减少求解时间。我们提出了一个大规模的实证应用，其中分析了美国生物燃料指令对农业和运输燃料部门的影响。由于模型的庞大规模和目标函数中涉及的非线性，两个强大的优化求解器无法处理该问题，而我们可以使用分解方法成功地求解经济均衡。