Primal-Dual Methods for Solving Infinite-Dimensional Games

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• 作者：Pavel Dvurechensky ; Yurii Nesterov…
• 关键词：Convex optimization ; Primal ; dual optimization methods ; Saddle ; point problems ; Differential games ; 90C06 ; 90C25 ; 90C60 ; 91A23 ; 49N70
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：166
• 期：1
• 页码：23-51
• 全文大小：582 KB
• 参考文献：1.Nesterov, Y.: Primal-dual subgradient methods for convex problems. Math. Program. 120(1), 221鈥?59 (2009)MATH MathSciNet View Article
  2.Devolder, O., Glineur, F., Nesterov, Y.: Double smoothing technique for large-scale linearly constrained convex optimization. SIAM J. Optim. 22(2), 702鈥?27 (2012)MATH MathSciNet View Article
  3.Antsaklis, P.J., Michel, A.N.: Linear Systems. Birkhauser Book, Boston (2006)MATH
  4.Maurice, S.: On general minimax theorems. Pac. J. Math. 8(1), 171鈥?76 (1958)MATH View Article
  5.Nesterov, Y.: Dual extrapolation and its applications for solving variational inequalities and related problems. J. Math. Program. Ser. B 109(2), 319鈥?44 (2007)MATH MathSciNet View Article
  
• 作者单位：Pavel Dvurechensky (1)
  Yurii Nesterov (2)
  Vladimir Spokoiny (3)
  
  1. PreMoLab, Moscow Institute of Physics and Technology, Institutskii st.,9, Dolgoprudny, Russia
  2. CORE, Universite catholique de Louvain, 1348, Louvain-la-Neuve, Belgium
  3. Weierstrass Institute and Humboldt University, Mohrenstr. 39, 10117, Berlin, Germany
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

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.