Connection of two approaches to the Fisher model

The article continues the author's research on the problem of finding equilibrium in economic exchange models. For the Fisher model, it was previously known that the equilibrium problem can be reduced to some optimization problem. This result was obtained by Gale and Eisenberg, while the final algorithms on this way were not found. The author proposed the original polyhedral complementarity approach, which generated an optimization problem of a different type. This approach made possible the development of finite algorithms for finding the equilibrium. So far, the equivalence of these two optimization problems has not been shown. However, it turned out that the dual problems obtained in a special way are equivalent. In this paper, a general scheme of duality for convex optimization problems is proposed. This scheme allows us to clarify the nature of duality and the relationship between the Gale–Eisenberg and the polyhedral complementarity approaches. Illustr. 1, bibliogr. 17.