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A Relaxed Approximate Proximal Point Algorithm

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  • Zhenhua Yang
  • Bingsheng He

Abstract

For a maximal monotone operator T, a well-known overrelaxed point algorithm is often used to find the zeros of T. In this paper, we enhance the algorithm to find a point in $T^{-1}(0)\cap \mathcal{X}$ , where $\mathcal{X}$ is a given closed convex set. In the inexact case of our modified relaxed proximal point algorithm, we give a new criterion. The convergence analysis is quite easy to follow. Copyright Springer Science + Business Media, Inc. 2005

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  • Zhenhua Yang & Bingsheng He, 2005. "A Relaxed Approximate Proximal Point Algorithm," Annals of Operations Research, Springer, vol. 133(1), pages 119-125, January.
    • Handle: RePEc:spr:annopr:v:133:y:2005:i:1:p:119-125:10.1007/s10479-004-5027-9
    DOI: 10.1007/s10479-004-5027-9
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    References listed on IDEAS

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    1. Jonathan Eckstein, 1993. "Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 202-226, February.
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    Cited by:

    1. Francisco Aragón Artacho & Michaël Gaydu, 2012. "A Lyusternik–Graves theorem for the proximal point method," Computational Optimization and Applications, Springer, vol. 52(3), pages 785-803, July.

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