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Ergodic Convergence in Proximal Point Algorithms with Bregman Functions

  • Osman Güler
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 1)

Abstract

We prove ergodic convergence results for the proximal point algorithm with Bregman kernels. In the function minimization case, the iterates converge to a minimizer of the function in the ergodic sense. We give global convergence rate estimate for the residual f(zk) — min f(x). In the general case of finding a zero of a maximal monotone operator T, our main result states that, under very general conditions, all limit points of the ergodic solution sequence converge to a zero of T. Under slightly less general conditions, we show that either the original solution sequence convergence to a zero of T, or it stays bounded away from the zero set of T.

Keywords

Nonexpansive Mapping Monotone Operator Maximal Monotone Maximal Monotone Operator Proximal Point Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Osman Güler
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of Maryland Baltimore CountyBaltimoreUSA

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