Primal-Dual Methods for Solving Infinite-Dimensional Games

Pavel Dvurechensky (), Yurii Nesterov () and Vladimir Spokoiny ()
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Pavel Dvurechensky: PreMoLab, Moscow Institute of Physics and Technology
Yurii Nesterov: Universite catholique de Louvain
Vladimir Spokoiny: Weierstrass Institute and Humboldt University

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 1, No 2, 23-51

Abstract: 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.

Keywords: Convex optimization; Primal-dual optimization methods; Saddle-point problems; Differential games; 90C06; 90C25; 90C60; 91A23; 49N70 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-015-0771-3

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