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Extragradient method for finding a saddle point in a multicriteria problem with dynamics

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Abstract

We consider an optimal control problem for a linear system of ordinary differential equations with an implicitly given boundary condition connected with a multicriteria problem. Such problems arise, for example, in the study of controlled objects that lose their stability under the influence of external perturbations, where it is required to return an object to stability by means of an appropriate choice of the control. We describe a possible mathematical model of this kind, propose an extragradient method for recovering the stability, and investigate its convergence.

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References

  1. F. P. Vasil’ev, Optimization Methods (MTsNMO, Moscow, 2011), Vols. 1, 2 [in Russian].

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  2. A. S. Antipin, E. V. Khoroshilova, “Multicriteria boundary value problem in dynamics,” Trudy Inst. Mat. Mekh. UrO RAN 21 (3), 20–29 (2015).

    MathSciNet  Google Scholar 

  3. V. V. Podinovskii and V. D. Nogin, Pareto-Optimal Solutions of Multicriteria Problems (Fizmatlit, Moscow, 2007) [in Russian].

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  4. A. S. Antipin, “On two formulations of equilibrium problems,” in Optimization and Applications (Vychisl. Tsentr Ross. Akad. Nauk, Moscow, 2011), issue 2, pp. 13–41 [in Russian].

    MathSciNet  Google Scholar 

  5. L. A. Artem’eva, “Extragradient method for searching an equilibrium point in two-person saddle-point games,” Comput. Math. Math. Phys. 51 (12), 2017–2030 (2011).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    F. P. Vasil’ev & L. A. Artem’eva

  2. Dorodnitsyn Computing Center of the Russian Academy of Sciences, Moscow, 119333, Russia

    A. S. Antipin

Authors
  1. F. P. Vasil’ev
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  2. A. S. Antipin
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  3. L. A. Artem’eva
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Corresponding author

Correspondence to F. P. Vasil’ev.

Additional information

Original Russian Text © F.P. Vasil’ev, A.S. Antipin, L.A. Artem’eva, 2016, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Vol. 22, No. 2.

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Vasil’ev, F.P., Antipin, A.S. & Artem’eva, L.A. Extragradient method for finding a saddle point in a multicriteria problem with dynamics. Proc. Steklov Inst. Math. 297 (Suppl 1), 203–210 (2017). https://doi.org/10.1134/S0081543817050224

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  • DOI: https://doi.org/10.1134/S0081543817050224

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