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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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