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Primal-Dual Methods for Solving Infinite-Dimensional Games

Author

Listed:
  • Pavel Dvurechensky

    (PreMoLab, Moscow Institute of Physics and Technology)

  • Yurii Nesterov

    (Universite catholique de Louvain)

  • Vladimir Spokoiny

    (Weierstrass Institute and Humboldt University)

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.

Suggested Citation

  • Pavel Dvurechensky & Yurii Nesterov & Vladimir Spokoiny, 2015. "Primal-Dual Methods for Solving Infinite-Dimensional Games," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 23-51, July.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:1:d:10.1007_s10957-015-0771-3
    DOI: 10.1007/s10957-015-0771-3
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    References listed on IDEAS

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    1. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2012. "Double smoothing technique for large-scale linearly constrained convex optimization," LIDAM Reprints CORE 2423, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Bruce Cox & Anatoli Juditsky & Arkadi Nemirovski, 2017. "Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 402-435, February.
    2. Fedor Stonyakin & Alexander Gasnikov & Pavel Dvurechensky & Alexander Titov & Mohammad Alkousa, 2022. "Generalized Mirror Prox Algorithm for Monotone Variational Inequalities: Universality and Inexact Oracle," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 988-1013, September.

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