Monotone operator theory in convex optimization

@article{Combettes2018MonotoneOT,
  title={Monotone operator theory in convex optimization},
  author={Patrick L. Combettes},
  journal={Mathematical Programming},
  year={2018},
  volume={170},
  pages={177-206}
}
  • P. L. Combettes
  • Published 8 February 2018
  • Mathematics
  • Mathematical Programming
Several aspects of the interplay between monotone operator theory and convex optimization are presented. The crucial role played by monotone operators in the analysis and the numerical solution of convex minimization problems is emphasized. We review the properties of subdifferentials as maximally monotone operators and, in tandem, investigate those of proximity operators as resolvents. In particular, we study new transformations which map proximity operators to proximity operators, and… 

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