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A viscosity method with no spectral radius requirements for the split common fixed point problem

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  • Maingé, Paul-Emile

Abstract

This paper is concerned with an algorithmic solution to the split common fixed point problem in Hilbert spaces. Our method can be regarded as a variant of the “viscosity approximation method”. Under very classical assumptions, we establish a strong convergence theorem with regard to involved operators belonging to the wide class of quasi-nonexpansive operators. In contrast with other related processes, our algorithm does not require any estimate of some spectral radius. The technique of analysis developed in this work is new and can be applied to many other fixed point iterations. Numerical experiments are also performed with regard to an inverse heat problem.

Suggested Citation

  • Maingé, Paul-Emile, 2014. "A viscosity method with no spectral radius requirements for the split common fixed point problem," European Journal of Operational Research, Elsevier, vol. 235(1), pages 17-27.
    • Handle: RePEc:eee:ejores:v:235:y:2014:i:1:p:17-27
    DOI: 10.1016/j.ejor.2013.11.028
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    References listed on IDEAS

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    1. Larsson, Torbjorn & Patriksson, Michael & Stromberg, Ann-Brith, 1996. "Conditional subgradient optimization -- Theory and applications," European Journal of Operational Research, Elsevier, vol. 88(2), pages 382-403, January.
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