Composite optimization for the resource allocation problem

TL;DR

This paper introduces an improved convex optimization approach for resource allocation, applying gradient methods to the dual problem, with proven faster convergence and economic interpretation of the algorithms.

Contribution

It presents novel accelerated gradient methods for resource allocation with enhanced convergence rates and an economic interpretation linking algorithmic steps to market adjustments.

Findings

Faster convergence rates than existing methods

Dual and primal iterates converge efficiently

Economic interpretation of gradient methods

Abstract

In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the convergence rate both for the primal iterates and the dual iterates. We obtain faster convergence rates than the ones known in the literature. We also provide economic interpretation for these two methods. This means that iterations of the algorithms naturally correspond to the process of price and production adjustment in order to obtain the desired production volume in the economy. Overall, we show how these actions of the economic agents lead the whole system to the equilibrium.