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Primal-dual methods for solving infinite-dimensional games

Dvurechensky, Pavel;Nesterov, Yurii;Spokoiny, Vladimir
(2015) Journal of Optimization Theory and Applications — Vol. 166, n° 1, p. 23-51 (2015)

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Authors
  • Dvurechensky, PavelPreMoLab, Moscow Institute of Physics and Technology
    Author
  • Nesterov, YuriiUCLouvain
    Author
  • Spokoiny, VladimirWeierstrass Institute and Humboldt University
    Author
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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Dvurechensky, P., Nesterov, Y., & Spokoiny, V. (2015). Primal-dual methods for solving infinite-dimensional games. Journal of Optimization Theory and Applications, 166(1), 23-51. https://doi.org/10.1007/s10957-015-0771-3 (Original work published 2015)