登入選單

返回Google圖書搜尋

Formulation and Solution of Economic Equilibrium Problems

John Charles StoneStanford University. Systems Optimization Laboratory

出版	Stanford University, 1988
URL	http://books.google.com.hk/books?id=QvQEAAAAIAAJ&hl=&source=gbs_api

註釋

This report develops and assess a number of equivalent mathematical formulations of the general equilibrium problem in economics. It begins with the traditional representation as a nonlinear complementarity problem and develop alternative representations as nonlinear optimization problems. All of our formulations depart from previous approaches by including an explicit linear equality for price normalization and a matched artificial variable which must be zero at any equilibrium solution. This structure has the theoretical and computational advantage that any linearization of the equilibrium problem has a feasible complementary solution. Moreover, under a reasonable rank condition, a basic complementary solution exists which can be successfully computed by Lemke's almost-complementary pivoting method. It describes five general-purpose methods which can be applied to solving the equilibrium problem. The common feature of these methods is solving a sequence of linearized problems. It establishes a number of equivalences between the methods, when applied to the equilibrium problem, and assess their local and global convergence properties in that context. An important new tool in this analysis is another problem formulation based on a differentiable exact penalty function. This formulation provides, perhaps for the first time, a rigorous means of evaluating the progress of a sequential method for computing an equilibrium solution. Our analysis reveals a basic theoretical dilemma in solving general equilibrium problems by these sequential methods. One group of methods produces iterates that converge from any starting point, but the sequence may converge to a non-equilibrium point. (SDW).