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

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.