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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 11, Pages 1969–1990 (Mi zvmmf566)  

This article is cited in 37 scientific papers (total in 37 papers)

An extraproximal method for solving equilibrium programming problems and games

A. S. Antipin

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: For equilibrium programming problems and two-person games defined on simple sets or sets given by functional inequality constraints, an extraproximal method is proposed and examined. The convergence of this method is proved.

Key words: equilibrium programming, two-person games, extraproximal method, convergence.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:11, 1893–1914

Bibliographic databases:
UDC: 519.6:519.83
Received: 17.05.2005

Citation: A. S. Antipin, “An extraproximal method for solving equilibrium programming problems and games”, Zh. Vychisl. Mat. Mat. Fiz., 45:11 (2005), 1969–1990; Comput. Math. Math. Phys., 45:11 (2005), 1893–1914

Citation in format AMSBIB
\by A.~S.~Antipin
\paper An extraproximal method for solving equilibrium programming problems and games
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 11
\pages 1969--1990
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 11
\pages 1893--1914

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. F. P. Vasil'ev, A. S. Antipin, “Methods for solving unstable equilibrium programming problems with coupled variables”, Proc. Steklov Inst. Math. (Suppl.), 253, suppl. 1 (2006), S229–S246  mathnet  crossref  mathscinet  zmath  elib
    2. A. S. Antipin, “Extraproximal approach to calculating equilibriums in pure exchange models”, Comput. Math. Math. Phys., 46:10 (2006), 1687–1698  mathnet  crossref  mathscinet
    3. A. S. Stukalov, “An extraproximal method for solving equilibrium programming problems in a Hilbert space”, Comput. Math. Math. Phys., 46:5 (2006), 743–761  mathnet  crossref  mathscinet
    4. A. S. Antipin, “Multicriteria equilibrium programming: Extraproximal methods”, Comput. Math. Math. Phys., 47:12 (2007), 1912–1927  mathnet  crossref  mathscinet
    5. Jiménez-Lizárraga M., Poznyak A., “Robust Nash equilibrium in multi-model LQ differential games: analysis and extraproximal numerical procedure”, Optimal Control Appl. Methods, 28:2 (2007), 117–141  crossref  mathscinet  isi  elib  scopus
    6. Alvarez I., Poznyak A., Malo A., “Urban traffic control problem via a game theory application”, Proceedings of the 46th IEEE Conference on Decision and Control, IEEE Conference on Decision and Control - Proceedings, 2007, 4979–4983  isi
    7. A. S. Antipin, “Saddle problem and optimization problem as an integrated system”, Proc. Steklov Inst. Math. (Suppl.), 263, suppl. 2 (2008), S3–S14  mathnet  crossref  zmath  isi  elib
    8. A. V. Zykina, “Inverse complementarity in a resource deficit model”, Comput. Math. Math. Phys., 48:11 (2008), 1971–1980  mathnet  crossref  mathscinet  isi
    9. Moya S., Poznyak A., “Numerical Methods for Stackelberg-Nash Equilibrium Calculation with Favorable and Unfavorable Followers”, 2008 5th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE 2008), 2008, 36–41  isi
    10. Moya S., Poznyak A., “Stackelberg-Nash Concept Applied to the Traffic Control Problem with a Dominating Intersection”, 2008 5th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE 2008), 2008, 313–318  isi
    11. A. S. Antipin, O. A. Popova, “Equilibrium model of a credit market: Statement of the problem and solution methods”, Comput. Math. Math. Phys., 49:3 (2009), 450–465  mathnet  crossref  mathscinet  isi
    12. Antipin A., “Multicriteria equilibrium programming problems and methods for their solutions”, Optimization, 58:7 (2009), 729–753  crossref  mathscinet  zmath  isi  elib  scopus
    13. Moya S., Poznyak A.S., “Extraproximal Method Application for a StackelbergNash Equilibrium Calculation in Static Hierarchical Games”, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 39:6 (2009), 1493–1504  crossref  isi  scopus
    14. Jiménez-Lizárraga M., Fridman L., “Robust Nash strategies based on integral sliding mode control for a two players uncertain linear affine-quadratic game”, International Journal of Innovative Computing, Information and Control, 5:2 (2009), 241–251  isi
    15. A. S. Strekalovsky, A. V. Orlov, A. V. Malyshev, “A local search for the quadratic-linear bilevel programming problem”, Num. Anal. Appl., 3:1 (2010), 59–70  mathnet  crossref
    16. Alvarez I., Poznyak A., “Game Theory Applied to Urban Traffic Control Problem”, International Conference on Control, Automation and Systems (Iccas 2010), 2010, 2164–2169  isi
    17. A. S. Antipin, L. A. Artem'eva, F. P. Vasil'ev, “Extraproximal method for solving two-person saddle-point games”, Comput. Math. Math. Phys., 51:9 (2011), 1472–1482  mathnet  crossref  mathscinet  isi
    18. A. S. Antipin, A. I. Golikov, E. V. Khoroshilova, “Sensitivity function: Properties and applications”, Comput. Math. Math. Phys., 51:12 (2011), 2000–2016  mathnet  crossref  mathscinet  isi
    19. A. S. Antipin, “Metod modifitsirovannoi funktsii Lagranzha dlya zadach optimalnogo upravleniya so svobodnym pravym kontsom”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 4:2 (2011), 27–44  mathnet
    20. A. V. Zykina, N. V. Melen'chuk, “Finite number of iterations in the two-step extragradient method”, Russian Math. (Iz. VUZ), 58:9 (2014), 62–65  mathnet  crossref
    21. Trejo K.K., Clempner J.B., Poznyak A.S., “A Stackelberg Security Game With Random Strategies Based on the Extraproximal Theoretic Approach”, Eng. Appl. Artif. Intell., 37 (2015), 145–153  crossref  isi  elib  scopus
    22. Moya S., Escobar J., “Stackelberg-Nash Equilibrium in a Traffic Control Problem At An Intersection on a Priority Road”, IMA J. Math. Control Inf., 32:1 (2015), 161–194  crossref  mathscinet  zmath  isi  elib  scopus
    23. Clempner J.B., Poznyak A.S., “Modeling the Multi-Traffic Signal-Control Synchronization: a Markov Chains Game Theory Approach”, Eng. Appl. Artif. Intell., 43 (2015), 147–156  crossref  isi  elib  scopus
    24. Trejo K.K., Clempner J.B., Poznyak A.S., “Computing the Stackelberg/Nash Equilibria Using the Extraproximal Method: Convergence Analysis and Implementation Details For Markov Chains Games”, Int. J. Appl. Math. Comput. Sci., 25:2 (2015), 337–351  crossref  mathscinet  zmath  isi  elib  scopus
    25. Clempner J.B., Poznyak A.S., “Conforming coalitions in Markov Stackelberg security games: Setting max cooperative defenders vs. non-cooperative attackers”, Appl. Soft. Comput., 47 (2016), 1–11  crossref  mathscinet  isi  elib  scopus
    26. Solis C.U., Clempner J.B., Poznyak A.S., “Modeling Multileader?Follower Noncooperative Stackelberg Games”, Cybern. Syst., 47:8 (2016), 650–673  crossref  isi  elib  scopus
    27. Trejo K.K., Clempner J.B., Poznyak A.S., “An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games”, Kybernetika, 52:2 (2016), 258–279  crossref  mathscinet  zmath  isi  elib  scopus
    28. Trejo K.K., Clempner J.B., Poznyak A.S., “Adapting Strategies to Dynamic Environments in Controllable Stackelberg Security Games”, 2016 IEEE 55Th Conference on Decision and Control (Cdc), IEEE Conference on Decision and Control, IEEE, 2016, 5484–5489  isi
    29. Trejo K.K., Clempner J.B., Poznyak A.S., Appl. Math. Model., 41 (2017), 399–418  crossref  mathscinet  isi  scopus
    30. Trejo K.K., Clempner J.B., Poznyak A.S., “Nash Bargaining Equilibria For Controllable Markov Chains Games”, IFAC PAPERSONLINE, 50:1 (2017), 12261–12266  crossref  isi  scopus
    31. Clempner J.B., Poznyak A.S., “Using the Extraproximal Method For Computing the Shortest-Path Mixed Lyapunov Equilibrium in Stackelberg Security Games”, Math. Comput. Simul., 138 (2017), 14–30  crossref  mathscinet  isi  scopus
    32. Clempner J.B., “A Game Theory Model For Manipulation Based on Machiavellianism: Moral and Ethical Behavior”, JASSS, 20:2 (2017), 12  crossref  isi  scopus
    33. Trejo K.K., Clempner J.B., Poznyak A.S., “Adapting Attackers and Defenders Patrolling Strategies: a Reinforcement Learning Approach For Stackelberg Security Games”, J. Comput. Syst. Sci., 95 (2018), 35–54  crossref  mathscinet  zmath  isi  scopus
    34. Clempner J.B., “A Continuous-Time Markov Stackelberg Security Game Approach For Reasoning About Real Patrol Strategies”, Int. J. Control, 91:11, SI (2018), 2494–2510  crossref  mathscinet  isi  scopus
    35. Dominguez F., Clempner J.B., “Multiperiod Mean-Variance Customer Constrained Portfolio Optimization For Finite Discrete-Time Markov Chains”, Econ. Comput. Econ. Cybern. Stud., 53:1 (2019), 39–56  crossref  isi
    36. Trejo K.K., Clempner J.B., Poznyak A.S., “Proximal Constrained Optimization Approach With Time Penalization”, Eng. Optimiz., 51:7 (2019), 1207–1228  crossref  isi
    37. Clempner J.B., “A Team Formation Method Based on a Markov Chains Games Approach”, Cybern. Syst., 50:5 (2019), 417–443  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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