Dual subgradient method with averaging for optimal resource allocation

Abstract

A dual subgradient method is proposed for solving convex optimization problems with linear constraints. As novelty, the recovering of primal solutions can be avoided. Instead, the optimal convergence rate for the whole sequence of primal-dual iterates is obtained. This is due to the primal-dual averaging strategies which are incorporated into the iterative scheme. We apply our dual subgradient method with averaging to optimal resource allocation within a multi-agent environment. The proposed dual subgradient method naturally corresponds to a distributed process of production/price adjustments and effectively leads to a market equilibrium.