Decomposition approach for solving large-scale spatially disaggregated economic equilibrium problems
本文用Dantzig-Wolfe分解法求解大规模非线性经济均衡问题，通过上下界偏差控制迭代终止，实证表明能大幅缩短求解时间，并成功应用于美国生物燃料政策对农业和交通燃料部门的影响分析。
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.