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We consider the resource allocation problem and its numerical solution. Thefollowing constructions are demonstrated: 1) Walrasian price-adjustmentmechanism for determining the equilibrium; 2) Decentralized role of the prices;3) Slater's method for price restrictions (dual Lagrange multipliers); 4) A newmechanism for determining equilibrium prices, in which prices are fullycontrolled not by Center (Government), but by economic agents -- nodes(factories). In economic literature the convergence of the considered methodsis only proved. In contrast, this paper provides an accurate analysis of theconvergence rate of the described procedures for determining the equilibrium.The analysis is based on the primal-dual nature of the suggested algorithms.More precisely, in this article we propose the economic interpretation of thefollowing numerical primal-dual methods of convex optimization: dichotomy andsubgradient projection method. Numerical experiments conclude the paper.

numerical analysis and applications

Walrasian Equilibrium and Centralized Distributed Optimization from the  point of view of Modern Convex Optimization Methods on the Example of  Resource Allocation Problem