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

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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.

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Authors and Affiliations

  1. Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong

    Chuangyin Dang

  2. Department of Management Science and Engineering, Stanford University, Stanford, CA, 94305, USA

    Yinyu Ye

  3. Departments of Applied Mathematics and Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hong Kong, Hong Kong

    Yinyu Ye

  4. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, 94305, USA

    Zhisu Zhu

Authors
  1. Chuangyin Dang
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  2. Yinyu Ye
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  3. Zhisu Zhu
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Correspondence to Zhisu Zhu.

Additional information

Research supported in part by GRF CityU 113308 of the Government of Hong Kong SAR, NSF grant DMS-0604513, and NSF GOALI Grant 0800151.

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Dang, C., Ye, Y. & Zhu, Z. An interior-point path-following algorithm for computing a Leontief economy equilibrium. Comput Optim Appl 50, 223–236 (2011). https://doi.org/10.1007/s10589-010-9332-8

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  • DOI: https://doi.org/10.1007/s10589-010-9332-8

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