Composite optimization for the resource allocation problem
Anastasiya Ivanova, Pavel Dvurechensky, Alexander Vladimirovich Gasnikov, Dmitry Kamzolov · Optimization methods & software · 2018
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints.To solve this problem, we use subgradient method and gradient descent applied to the dual problem and prove the convergence rate both for the primal iterates and the dual iterates.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.