On Accelerated Coordinate Descent Methods for Searching Equilibria in Two-Stage Transportation Equilibrium Traffic Flow Distribution Model

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, it is proposed to use the accelerated block-coordinate Nesterov–Stich method with a...

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Bibliographic Details
Published in:Programming and computer software 2023-12, Vol.49 (6), p.513-524
Main Authors: Il’tyakov, N. A., Obozov, M. A., Dyshlevski, I. M., Yarmoshik, D. V., Kubentaeva, M. B., Gasnikov, A. V., Gasnikova, E. V.
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Computer Science
Convex analysis
Convexity
Costs
Entropy
Equilibrium
Equilibrium methods
Estimates
Flow distribution
Iterative methods
Linear programming
Numerical analysis
Operating Systems
Optimization
Software Engineering
Software Engineering/Programming and Operating Systems
Traffic flow
Traffic models
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Summary: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, it is proposed 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 appreciably 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.
ISSN:0361-7688
1608-3261
DOI:10.1134/S036176882306004X