1 of 10

Dynamical System Modeling and Stability Investigation�DSMSI-2023

Dedicated to the 77th anniversary of the outstanding Ukrainian scientist

professor Denys Khusainov

December 19-21, 2023, Kyiv, Ukraine

Optimizing network economics problem with adaptive algorithms for variational inequalities

Volodymyr Semenov, Serhii Denysov, �Taras Shevchenko National University of Kyiv

2 of 10

Blood supply network structure

Dynamical System Modeling and Stability Investigation, DSMSI-2023

3 of 10

Model formulation

Dynamical System Modeling and Stability Investigation, DSMSI-2023

In terms of link flows:

In terms of path flows:

Path flows costs through the link flows:

4 of 10

Variational inequality formulation

Dynamical System Modeling and Stability Investigation, DSMSI-2023

5 of 10

Extragradient algorithms

Dynamical System Modeling and Stability Investigation, DSMSI-2023

Two operator calculations, two projections, requires Lipschitz constant.

Historically first:

6 of 10

Extragradient algorithms – lean

Dynamical System Modeling and Stability Investigation, DSMSI-2023

7 of 10

Extragradient algorithms – adaptive

Dynamical System Modeling and Stability Investigation, DSMSI-2023

8 of 10

Software suite – problem editor

Dynamical System Modeling and Stability Investigation, DSMSI-2023

9 of 10

Software suite – results view

Dynamical System Modeling and Stability Investigation, DSMSI-2023

10 of 10

Thank you for your attention

Q&A

Serhii Denysov denisov.univ@gmail.com

�Volodymyr Semenov semenov.volodya@gmail.com