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.

中文翻译：

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基于资源分配问题的现代凸优化方法的瓦尔拉斯均衡和集中分布优化

考虑了资源分配问题及其数值解。证明了以下几点：（1）确定均衡状态的瓦尔拉斯价格调整机制；（2）价格的分散作用；（3）Slater的价格限制方法（双重拉格朗日乘数）；（4）确定均衡价格的新机制，其中价格完全由经济主体（节点（企业））而非中心（政府）控制。在经济文献中，仅证明了所考虑方法的收敛性。相反，本文提供了用于确定平衡的上述过程的收敛速度的准确分析。该分析基于所提出算法的原始对偶性质。更准确地说，在本文中，