On accelerated coordinate descent methods for searching equilibria in two-stage transportation equilibrium traffic flow distribution model

TL;DR

This paper introduces an accelerated block-coordinate Nesterov-Stich method for solving nonsmooth convex optimization problems in two-stage traffic equilibrium models, showing potential for improved convergence estimates.

Contribution

The paper proposes a novel accelerated coordinate descent algorithm tailored for two-stage transportation equilibrium problems, with theoretical complexity analysis and numerical validation.

Findings

The proposed method has better theoretical complexity bounds than previous approaches.

Numerical experiments demonstrate the effectiveness of the accelerated method.

The approach can potentially improve convergence speed in practical traffic flow models.

Abstract

The search for equilibrium in a two-stage traffic flow model reduces to the solution of a special nonsmooth convex optimization problem with two groups of different variables. For numerical solution of this problem, the paper proposes to use the accelerated block-coordinate Nesterov-Stich method with a special choice of block probabilities at each iteration. Theoretical estimates of the complexity of this approach can markedly improve the estimates of previously used approaches. However, in the general case they do not guarantee faster convergence. Numerical experiments with the proposed algorithms are carried out in the paper.