Composite optimization for the resource allocation problem. (4th July 2021)

• Record Type: Journal Article
• Authors: Ivanova, Anastasiya; Dvurechensky, Pavel; Gasnikov, Alexander; Kamzolov, Dmitry
• Is Part Of: Optimization methods and software. Volume 36:Number 4(2021)
• Page Start: 720
• Page End: 754
• Publication Date: 2021-07-04
• Subjects: Decentralized pricing -- primal–dual method -- accelerated gradient method -- gradient method -- composite optimization; 90C25 -- 68Q25 -- 91B32; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1712599
• Languages: English
• ISSNs: 1055-6788

Abstract

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.