Subgradient methods for huge-scale optimization problems

@article{Nesterov2014SubgradientMF,
  title={Subgradient methods for huge-scale optimization problems},
  author={Yurii Nesterov},
  journal={Mathematical Programming},
  year={2014},
  volume={146},
  pages={275-297}
}
  • Y. Nesterov
  • Published 1 August 2014
  • Mathematics, Computer Science
  • Mathematical Programming
We consider a new class of huge-scale problems, the problems with sparse subgradients. The most important functions of this type are piece-wise linear. For optimization problems with uniform sparsity of corresponding linear operators, we suggest a very efficient implementation of subgradient iterations, which total cost depends logarithmically in the dimension. This technique is based on a recursive update of the results of matrix/vector products and the values of symmetric functions. It works… 
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