publication . Other literature type . Article . 1976

Monotone Operators and the Proximal Point Algorithm

R. Tyrrell Rockafellar;
Open Access
  • Published: 01 Aug 1976
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
Abstract
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 is investigated here in a more general form where the requirement for exact minimization at each iteration is weakened, and the subdifferential $\partial f$ is replaced by...
Subjects
free text keywords: Control and Optimization, Applied Mathematics, Strongly monotone, Hadamard space, Duality (optimization), Rate of convergence, Monotone polygon, Hilbert space, symbols.namesake, symbols, Discrete mathematics, Proximal Gradient Methods, Algorithm, Mathematics, Subderivative
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