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Primal-Dual Methods for Solving Infinite-Dimensional Games

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Abstract

In this paper, we show that the infinite-dimensional differential games with simple objective functional can be solved in a finite-dimensional dual form in the space of dual multipliers for the constraints related to the end points of the trajectories. The primal solutions can be easily reconstructed by the appropriate dual subgradient schemes. The suggested schemes are justified by the worst-case complexity analysis.

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Notes

  1. Since the objective and the feasible set of our problem are simple, very often this can be done in an explicit form.

References

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Acknowledgments

The research presented in this paper was partially supported by the Laboratory of Structural Methods of Data Analysis in Predictive Modeling, MIPT, through the RF government Grant, ag.11.G34.31.0073 and by RFBR, Research Project No. 13-01-12007 ofi_m.

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Authors and Affiliations

  1. PreMoLab, Moscow Institute of Physics and Technology, Institutskii st.,9, Dolgoprudny, Russia

    Pavel Dvurechensky

  2. CORE, Universite catholique de Louvain, 1348, Louvain-la-Neuve, Belgium

    Yurii Nesterov

  3. Weierstrass Institute and Humboldt University, Mohrenstr. 39, 10117, Berlin, Germany

    Vladimir Spokoiny

Authors
  1. Pavel Dvurechensky
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  2. Yurii Nesterov
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  3. Vladimir Spokoiny
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Corresponding author

Correspondence to Yurii Nesterov.

Additional information

Communicated by Boris S. Mordukhovich.

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Dvurechensky, P., Nesterov, Y. & Spokoiny, V. Primal-Dual Methods for Solving Infinite-Dimensional Games. J Optim Theory Appl 166, 23–51 (2015). https://doi.org/10.1007/s10957-015-0771-3

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  • DOI: https://doi.org/10.1007/s10957-015-0771-3

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