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Convergence Theorems of Modified Proximal Algorithms for Asymptotical Quasi-nonexpansive Mappings in CAT(0) Spaces

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  • Shengquan Weng
  • Dingping Wu

Abstract

In this paper, a new modified proximal point algorithm involving fixed point iterates of a finite number of asymptotically quasi-nonexpansive mappings in $CAT(0)$ spaces is proposed and been proved for the existence of a sequence generated by our iterative process converging to a minimizer of a convex function and a commen fixed point of a finite number of asymptotically quasi-nonexpansive mappings.

Suggested Citation

  • Shengquan Weng & Dingping Wu, 2018. "Convergence Theorems of Modified Proximal Algorithms for Asymptotical Quasi-nonexpansive Mappings in CAT(0) Spaces," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(2), pages 66-76, April.
    • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:2:p:66
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    References listed on IDEAS

    as
    1. H.K. Xu, 2003. "An Iterative Approach to Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 659-678, March.
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    More about this item

    Keywords

    convex minimization problem; $CAT(0)$ spaces; resolvent identity; asymptotically quasi-nonexpansive mapping; proximal point algorithm;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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