Curse of dimensionality reduction in max-plus based approximation methods: Theoretical estimates and improved pruning algorithms

@article{Gaubert2011CurseOD,
  title={Curse of dimensionality reduction in max-plus based approximation methods: Theoretical estimates and improved pruning algorithms},
  author={St{\'e}phane Gaubert and William M. McEneaney and Zheng Qu},
  journal={IEEE Conference on Decision and Control and European Control Conference},
  year={2011},
  pages={1054-1061}
}
Max-plus based methods have been recently developed to approximate the value function of possibly high dimensional optimal control problems. A critical step of these methods consists in approximating a function by a supremum of a small number of functions (max-plus “basis functions”) taken from a prescribed dictionary. We study several variants of this approximation problem, which we show to be continuous versions of the facility location and k-center combinatorial optimization problems, in… CONTINUE READING

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