The Walrasian Equilibrium and Centralized Distributed Optimization in Terms of Modern Convex Optimization Methods by an Example of the Resource Allocation Problem
E. A. Vorontsova, A. V. Gasnikov, A. S. Ivanova, E. A. Nurminsky · Numerical Analysis and Applications · 2019
The resource allocation problem and its numerical solution are considered. The following is demonstrated: (1) Walrasian price-adjustment mechanism for determining the equilibrium state; (2) decentralized role of prices; (3) Slater’s method for price restrictions (dual Lagrange multipliers); (4) new mechanism for determining equilibrium prices, in which prices are fully controlled by economic agents—nodes (enterprises)—rather than by the Center (Government). In the economic literature, only the convergence of the methods considered is proved. In contrast, this paper provides an accurate analysis of the convergence rate of the described procedures for determining the equilibrium. The analysis is based on the primal-dual nature of the algorithms proposed. More precisely, in this paper, we propose the economic interpretation of the following numerical primal-dual methods of convex optimization: dichotomy and subgradient projection method.