Efficient calculation of stochastic equilibriums in the Beckmann's and stable dynamic models

TL;DR

This paper introduces a composite approach for efficiently computing stochastic equilibriums in Beckmann's and stable dynamic models by reformulating the optimization problem and applying graph-based techniques to the dual problem.

Contribution

It presents a novel composite method that simplifies the calculation of stochastic equilibriums in specific convex optimization models with entropy regularization.

Findings

Enhanced computational efficiency for equilibrium calculation

Effective reformulation of the optimization problem

Application of graph-based techniques to dual problems

Abstract

We propose composite approache to the special sum-type convex optimization problem with affine restriction and special entropy type regularization. Since the fuctional has a penalty type form, we reformulate initial conditional optimization problem in a special unconstrained form that allows us to put the penalty type functional into the composite term. We also describe the characteristic functions on graphs technique (Yu. Nesterov, 2007) in application to the dual problem.