Monotone Operators and the Proximal Point Algorithm

@article{Rockafellar1976MonotoneOA,
  title={Monotone Operators and the Proximal Point Algorithm},
  author={R. Tyrrell Rockafellar},
  journal={Siam Journal on Control and Optimization},
  year={1976},
  volume={14},
  pages={877-898}
}
  • R. Rockafellar
  • Published 1 August 1976
  • Mathematics
  • Siam Journal on Control and Optimization
For the problem of minimizing a lower semicontinuous proper convex function f on a Hilbert space, the proximal point algorithm in exact form generates a sequence $\{ z^k \} $ by taking $z^{k + 1} $ to be the minimizes of $f(z) + ({1 / {2c_k }})\| {z - z^k } \|^2 $, where $c_k > 0$. This algorithm is of interest for several reasons, but especially because of its role in certain computational methods based on duality, such as the Hestenes-Powell method of multipliers in nonlinear programming. It… 

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