Primal-Dual Methods for Solving Infinite-Dimensional Games
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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.
KeywordsConvex optimization Primal-dual optimization methods Saddle-point problems Differential games
Mathematics Subject Classification90C06 90C25 90C60 91A23 49N70
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.