Searching equillibriums in Beckmann's and Nesterov--de Palma's models

TL;DR

This paper enhances classical algorithms for Beckmann's models and introduces a randomized dual averaging method for Nesterov--de Palma's models, providing convergence rates and potential optimality of these estimates.

Contribution

It develops a faster implementation of the Frank--Wolf algorithm for Beckmann's models and proposes a novel randomized dual averaging method for Nesterov--de Palma's models.

Findings

Improved convergence rates for Beckmann's models.

New randomized dual averaging method with proven convergence.

Estimates likely optimal without additional assumptions.

Abstract

In this paper we propose and develop classical Frank--Wolf algorithm for Beckmann's type models. This is not new, but we investigate details that allows us to speed up. We also consider stable dynamic like models. First model of this type was proposed 15 years ago by Yu. Nesterov and A. DePalma. We propose randomized dual averaging method with special (sum-type) randomization. For both of the problems we obtain the rates of convergences. It seems that this estimations to be unimprovable without additional assumption about problem formulation.