Tarasyev, Alexander Mikhailovich

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Total publications: 33
Scientific articles: 32
Presentations: 5

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Doctor of physico-mathematical sciences (1996)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 23.02.1959
Keywords: dynamic systems; optimal control theory; viscosity solutions of Hamilton–Jacobi equations; differential games; mathematical economics.


Grid schemes for constructing value functions and guaranteeing feedbacks are elaborated for optimal control problems. Finite difference operators based on constructions of nonsmooth analysis are proposed for approximation of generalized derivatives in Hamilton–Jacobi equations. Convergence results for approximation schemes are proved and estimates of convergence are indicated. Differential inequalities in terms of conjugate derivatives are obtaibed for characterization of stability properties of the value function in infinitesimal form. Regularity conditions for the function of programming maximin are derived in terms of conjugate variables. These results are applied to solution of a series of problems of mathematical economics: dynamic bimatrix games, models of optimal economic growth, problems of dynamic vector optimization, game interaction of investment projects, repeating games of auction type for searching optimal solutions of multicriteria problems.


Graduated from Faculty of Mathematics and Mechanics of Ural State University in 1981 (department of applied mathematics). Ph.D. thesis was defended in 1984. D.Sci. thesis was defended in 1996. A list of my works contains more than 100 titles. I have a part-time position in the Dynamic Systems project headed by A. V. Kryazhimskii at the International Institute for Applied Systems Analysis (IIASA, Laxenburg, Austria). I coordinate the program "Technology Innovation" organized at IIASA by the Committee of Systems Analysis of RAS.

In 1981 I was awarded the prize of the Ministry of Higher Education of Russian Federation for the masters's thesis devoted to algorithms for construction of resolving strategies in optimal control theory. In 1988 I received the prize of the Presidium of the Ural Branch of RAS and Sverdlovsk Komsomol organization for a series of papers on generalized solutions of Hamilton–Jacobi equations. In 1994 I won the Peccei prize of the International Institute for Applied Systems Analysis (IIASA, Laxenburg, Austria) for the research on dynamic bimatrix games.

Main publications:
  • Tarasyev A. M. Control Synthesis in Grid Schemes for Hamilton–Jacobi Equations. Annals of Operations Research, 1999, 88, 337–359.
  • Tarasyev A. M., Watanabe C. Optimal Dynamics of Innovation in Models of Economic Growth // Journal of Optimization Theory and Applications, 2001, 108(1), 175–203.
  • Tarasyev A. M., Watanabe C. Dynamic Optimality Principles and Sensitivity Analysis in Models of Economic Growth // Nonlinear Analysis, 2001, 47(4), 2309–2320.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. Nikolay A. Krasovskii, Alexander M. Tarasyev, “Mechanism for shifting Nash equilibrium trajectories to cooperative Pareto solutions in dynamic bimatrix games”, Contributions to Game Theory and Management, 13 (2020),  218–243  mathnet
2. Alexander M. Tarasyev, Anastasiia A. Usova, “An estimate of a smooth approximation of the production function for integrtaing Hamiltonian systems”, Mat. Teor. Igr Pril., 12:1 (2020),  91–115  mathnet
3. A. L. Bagno, A. M. Tarasyev, “Numerical methods for construction of value functions in optimal control problems on an infinite horizon”, Izv. IMI UdGU, 53 (2019),  15–26  mathnet  elib
4. A. L. Bagno, A. M. Tarasyev, “Estimate for the Accuracy of a Backward Procedure for the Hamilton–Jacobi Equation in an Infinite-Horizon Optimal Control Problem”, Trudy MIAN, 304 (2019),  123–136  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 304 (2019), 110–123  isi  scopus
5. A. L. Bagno, A. M. Tarasyev, “Discrete approximation of the Hamilton-Jacobi equation for the value function in an optimal control problem with infinite horizon”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:1 (2018),  27–39  mathnet  elib
6. A. L. Bagno, A. M. Tarasyev, “Asymptotics of value function in models of economic growth”, Tambov University Reports. Series: Natural and Technical Sciences, 23:124 (2018),  605–616  mathnet  elib
7. A. L. Bagno, A. M. Tarasyev, “Stability properties of the value function in an infinite horizon optimal control problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:1 (2017),  43–56  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 1–14  isi
8. N. A. Krasovskii, A. M. Tarasyev, “Asymptotic behavior of solutions in dynamical bimatrix games with discounted indices”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:2 (2017),  193–209  mathnet  elib
9. A. A. Krasovskii, P. D. Lebedev, A. M. Tarasyev, “Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints”, Zh. Vychisl. Mat. Mat. Fiz., 57:5 (2017),  768–782  mathnet  mathscinet  elib; Comput. Math. Math. Phys., 57:5 (2017), 770–783  isi  scopus
10. Alexandr M. Tarasyev, Anastasiya A. Usova, Yuliya V. Shmotina, “Predictive trajectories of economic development under structural changes”, Mat. Teor. Igr Pril., 8:3 (2016),  34–66  mathnet
11. Nikolay A. Krasovskii, Alexander M. Tarasyev, “Equilibrium trajectories in dynamical bimatrix games with average integral payoff functionals”, Mat. Teor. Igr Pril., 8:2 (2016),  58–90  mathnet; Autom. Remote Control, 79:6 (2018), 1148–1167  isi
12. A. A. Krasovskii, P. D. Lebedev, A. M. Tarasyev, “Some facts about the Ramsey model”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:3 (2016),  160–168  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 123–131  isi  scopus
13. A. L. Bagno, A. M. Tarasyev, “Properties of the value function in optimal control problems with infinite horizon”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:1 (2016),  3–14  mathnet  mathscinet  elib
14. A. V. Kryazhimskiy, A. M. Tarasyev, “Optimal control for proportional economic growth”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:2 (2015),  115–133  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 101–119  isi  scopus
15. A. V. Kryazhimskiy, A. M. Tarasyev, A. A. Usova, W. Wang, “Proportional economic growth under conditions of limited natural resources”, Trudy MIAN, 291 (2015),  138–156  mathnet  elib; Proc. Steklov Inst. Math., 291 (2015), 127–145  isi  scopus
16. A. M. Taras'ev, A. A. Usova, W. Wang, O. V. Russkikh, “Optimal trajectory construction by integration of Hamiltonian dynamics in models of economic growth under resource constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:4 (2014),  258–276  mathnet  mathscinet  elib
17. N. A. Krasovskiy, A. V. Kryazhimskiy, A. M. Tarasyev, “Hamilton–Jacobi equations in evolutionary games”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:3 (2014),  114–131  mathnet  mathscinet  elib
18. A. M. Tarasyev, A. A. Usova, “Stabilizing the Hamiltonian system for constructing optimal trajectories”, Trudy MIAN, 277 (2012),  257–274  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 277 (2012), 248–265  isi  elib  scopus
19. Nikolay A. Krasovskiy, Alexander M. Tarasyev, “Decomposition algorithm of searching equilibria in the dynamical game”, Mat. Teor. Igr Pril., 3:4 (2011),  49–88  mathnet; Autom. Remote Control, 76:10 (2015), 1865–1893
20. A. M. Tarasyev, A. A. Usova, “Influence of production function parameters on the solution and value function in optimal control problem”, Mat. Teor. Igr Pril., 3:3 (2011),  85–115  mathnet
21. A. M. Tarasyev, A. A. Usova, “Nonlinear stabilizer constructing for two-sector economic growth model”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:5 (2010),  297–307  mathnet  elib
22. A. M. Tarasyev, A. A. Usova, “Construction of a regulator for the Hamiltonian system in a two-sector economic growth model”, Trudy MIAN, 271 (2010),  278–298  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 271 (2010), 265–285  isi  elib  scopus
23. N. A. Krasovskii, A. M. Tarasyev, “Search of maximum points for a vector criterion based on decomposition properties”, Trudy Inst. Mat. i Mekh. UrO RAN, 15:4 (2009),  167–182  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S174–S190  scopus
24. A. A. Krasovskii, A. M. Taras'ev, “Construction of nonlinear regulators in economic growth models”, Trudy Inst. Mat. i Mekh. UrO RAN, 15:3 (2009),  127–138  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S143–S154  isi  scopus
25. A. A. Krasovskii, A. M. Tarasyev, “Properties of Hamiltonian Systems in the Pontryagin Maximum Principle for Economic Growth Problems”, Trudy MIAN, 262 (2008),  127–145  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 262 (2008), 121–138  isi  elib  scopus
26. A. A. Krasovskii, A. M. Tarasyev, “Optimization of the stopping time in multilevel dynamic systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, 2,  63–64  mathnet
27. A. A. Krasovskii, A. M. Tarasyev, “Dynamic optimization of investments in the economic growth models”, Avtomat. i Telemekh., 2007, 10,  38–52  mathnet  mathscinet  zmath; Autom. Remote Control, 68:10 (2007), 1765–1777  scopus
28. S. M. Aseev, A. V. Kryazhimskii, A. M. Tarasyev, “The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval”, Trudy MIAN, 233 (2001),  71–88  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 233 (2001), 64–80
29. S. V. Grigor'eva, A. M. Tarasyev, A. A. Uspenskii, V. N. Ushakov, “Constructions of the differential game theory for solving the Hamilton–Jacobi equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 6:2 (2000),  320–336  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2000no. , suppl. 2, S38–S53
30. A. V. Kryazhimskii, A. Nentjes, S. V. Shibaev, A. M. Tarasyev, “A game model of negotiations and market equilibria”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 61 (1999),  15–32  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 100:6 (2000), 2601–2612
31. A. M. Tarasyev, V. N. Ushakov, A. P. Khripunov, “On construction of positional absorption set in conflict control problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 1 (1992),  160–177  mathnet  mathscinet  zmath  elib
32. A. I. Subbotin, A. M. Tarasyev, “Conjugate derivatives of the value function of a differential game”, Dokl. Akad. Nauk SSSR, 283:3 (1985),  559–564  mathnet  mathscinet  zmath

33. Sergei M. Aseev, Alexander G. Chentsov, Alexey A. Davydov, Nikolai L. Grigorenko, Vyacheslav I. Maksimov, Elena A. Rovenskaya, Alexander M. Tarasiev, “In memory of Arkady Viktorovich Kryazhimskiy (1949-2014)”, Ural Math. J., 2:2 (2016),  3–15  mathnet  zmath  elib

Presentations in Math-Net.Ru
1. Региональный научно-образовательный математический центр «Уральский математический центр»
A. M. Tarasyev
General Meeting of the Branch of Mathematical Sciences, RAS, 2021
April 19, 2021 13:00   
2. Asymptotic stabilizers in problems of optimal economic development
A. M. Tarasyev, A. A. Usova
International conference "Systems Analysis: Modeling and Control" in memory of Academician A. V. Kryazhimskiy
May 31, 2018 15:00   
3. Opening of the Conference
N. L. Grigorenko, E. I. Moiseev, A. D. Gvishiani, E. A. Rovenskaya, S. M. Aseev, A. M. Tarasyev, A. A. Davydov, V. I. Maksimov, A. G. Chentsov
International conference "Systems Analysis: Modeling and Control" in memory of Academician A. V. Kryazhimskiy
May 31, 2018 09:30   
4. On solutions of approaching problems for controlled systems on a finite time interval
V. N. Ushakov, A. M. Tarasyev, A. V. Ushakov, V. I. Ukhobotov
International conference "Dynamical Systems: Inverse Problems, Stability and Control Processes" dedicated to the 80th birthday of Yu. S. Osipov
September 23, 2016 13:20   
5. Adaptive economic growth
A. V. Kryazhimskiy, A. M. Tarasyev
Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin
September 25, 2013 17:20   

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