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Convergence Analysis of Processes with Valiant Projection Operators in Hilbert Space

Author

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  • Yair Censor

    (University of Haifa)

  • Rafiq Mansour

    (University of Haifa)

Abstract

Convex feasibility problems require to find a point in the intersection of a finite family of convex sets. We propose to solve such problems by performing set-enlargements and applying a new kind of projection operators called valiant projectors. A valiant projector onto a convex set implements a special relaxation strategy, proposed by Goffin in 1971, that dictates the move toward the projection according to the distance from the set. Contrary to past realizations of this strategy, our valiant projection operator implements the strategy in a continuous fashion. We study properties of valiant projectors and prove convergence of our new valiant projections method. These results include as a special case and extend the 1985 automatic relaxation method of Censor.

Suggested Citation

  • Yair Censor & Rafiq Mansour, 2018. "Convergence Analysis of Processes with Valiant Projection Operators in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 35-56, January.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:1:d:10.1007_s10957-017-1174-4
    DOI: 10.1007/s10957-017-1174-4
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    References listed on IDEAS

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    1. Heinz H. Bauschke & Valentin R. Koch & Hung M. Phan, 2016. "Stadium Norm and Douglas-Rachford Splitting: A New Approach to Road Design Optimization," Operations Research, INFORMS, vol. 64(1), pages 201-218, February.
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    Cited by:

    1. Howard Heaton & Yair Censor, 2019. "Asynchronous sequential inertial iterations for common fixed points problems with an application to linear systems," Journal of Global Optimization, Springer, vol. 74(1), pages 95-119, May.

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