On the zero point problem of monotone operators in Hadamard spaces View Full Text


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Article Info

DATE

2019-04

AUTHORS

G. Zamani Eskandani, M. Raeisi

ABSTRACT

In this paper, by using products of finitely many resolvents of monotone operators, we propose an iterative algorithm for finding a common zero of a finite family of monotone operators and a common fixed point of an infinitely countable family of nonexpansive mappings in Hadamard spaces. We derive the strong convergence of the proposed algorithm under appropriate conditions. A common fixed point of an infinitely countable family of quasi-nonexpansive mappings and a common zero of a finite family of monotone operators are also approximated in reflexive Hadamard spaces. In addition, we define a norm on X◇ := spanX∗ and give an application of this norm, where X is an Hadamard space with dual space X∗. A numerical example to solve a nonconvex optimization problem will be exhibited in an Hadamard space to support our main results. More... »

PAGES

1155-1179

References to SciGraph publications

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  • 1979-03. Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces in ISRAEL JOURNAL OF MATHEMATICS
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  • 2008-12. Strong Convergence of Projected Subgradient Methods for Nonsmooth and Nonstrictly Convex Minimization in SET-VALUED ANALYSIS
  • 2013-12. Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2005-01. Singularities of Monotone Vector Fields and an Extragradient-type Algorithm in JOURNAL OF GLOBAL OPTIMIZATION
  • 2014-12. The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces in JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
  • 2016-12. A projection method for approximating fixed points of quasinonexpansive mappings in Hadamard spaces in FIXED POINT THEORY AND APPLICATIONS
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  • 2006-05. Convex- and Monotone-Transformable Mathematical Programming Problems and a Proximal-Like Point Method in JOURNAL OF GLOBAL OPTIMIZATION
  • Journal

    TITLE

    Numerical Algorithms

    ISSUE

    4

    VOLUME

    80

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11075-018-0521-3

    DOI

    http://dx.doi.org/10.1007/s11075-018-0521-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1103607703


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    48 schema:description In this paper, by using products of finitely many resolvents of monotone operators, we propose an iterative algorithm for finding a common zero of a finite family of monotone operators and a common fixed point of an infinitely countable family of nonexpansive mappings in Hadamard spaces. We derive the strong convergence of the proposed algorithm under appropriate conditions. A common fixed point of an infinitely countable family of quasi-nonexpansive mappings and a common zero of a finite family of monotone operators are also approximated in reflexive Hadamard spaces. In addition, we define a norm on X◇ := spanX∗ and give an application of this norm, where X is an Hadamard space with dual space X∗. A numerical example to solve a nonconvex optimization problem will be exhibited in an Hadamard space to support our main results.
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