An interior-point path-following algorithm for computing a Leontief economy equilibrium

Authors:
Chuangyin Dang;Yinyu Ye;Zhisu Zhu
Affiliations:
Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong;Department of Management Science and Engineering, Stanford University, Stanford, USA 94305 and Departments of Applied Mathematics and Logistics and Maritime Studies, The Hong Kong Polytechnic Univ ...;Institute for Computational and Mathematical Engineering, Stanford University, Stanford, USA 94305
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

In this paper, we present an interior-point path-following algorithm for computing a Leontief economy equilibrium, that is, an exchange market equilibrium with Leontief utility functions, which is known to be in the complexity class of PPAD-complete. It is known that an equilibrium corresponds to a solution of a system of complementarities, so we construct a smooth homotopy interior-point path to tackle this system. We prove that there always exists a continuously differentiable path leading to a complementary solution of the nonlinear system and at the same time to a Leontief economy equilibrium associated with the solution. We also report preliminary computational results to show effectiveness of the path-following Newton method.