# Ball intersection model for Fejér zones of convex closed sets

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2001)

- Volume: 21, Issue: 1, page 51-79
- ISSN: 1509-9407

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topDieter Schott. "Ball intersection model for Fejér zones of convex closed sets." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 21.1 (2001): 51-79. <http://eudml.org/doc/271553>.

@article{DieterSchott2001,

abstract = {Strongly Fejér monotone mappings are widely used to solve convex problems by corresponding iterative methods. Here the maximal of such mappings with respect to set inclusion of the images are investigated. These mappings supply restriction zones for the successors of Fejér monotone iterative methods. The basic tool is the representation of the images by intersection of certain balls.},

author = {Dieter Schott},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {set-valued mappings; Fejér monotone mappings; relaxations; central stretching; convex sets; ball intersections; iterative methods; convex problems; Fejér zones},

language = {eng},

number = {1},

pages = {51-79},

title = {Ball intersection model for Fejér zones of convex closed sets},

url = {http://eudml.org/doc/271553},

volume = {21},

year = {2001},

}

TY - JOUR

AU - Dieter Schott

TI - Ball intersection model for Fejér zones of convex closed sets

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2001

VL - 21

IS - 1

SP - 51

EP - 79

AB - Strongly Fejér monotone mappings are widely used to solve convex problems by corresponding iterative methods. Here the maximal of such mappings with respect to set inclusion of the images are investigated. These mappings supply restriction zones for the successors of Fejér monotone iterative methods. The basic tool is the representation of the images by intersection of certain balls.

LA - eng

KW - set-valued mappings; Fejér monotone mappings; relaxations; central stretching; convex sets; ball intersections; iterative methods; convex problems; Fejér zones

UR - http://eudml.org/doc/271553

ER -

## References

top- [1] I.I. Eremin and V.D. Mazurov, Nestacionarnye Processy Programmirovanija, Nauka, Moskva 1979.
- [2] J.-P. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms I, Springer-Verlag, Berlin et. al. 1993.
- [3] J.T. Marti, Konvexe Analysis, Birkhäuser Verlag, Basel 1977.
- [4] R.T. Rockafellar, Convex Analysis, Princeton, New Jersey 1972. Zbl0224.49003
- [5] D. Schott, Iterative solution of convex problems by Fejér monotone methods, Numer. Funct. Anal. Optimiz. 16 (1995), 1323-1357. Zbl0853.65055
- [6] D. Schott, Basic properties of Fejér monotone sequences, Rostock. Math. Kolloq. 49 (1995), 57-74. Zbl0855.65056
- [7] D. Schott, Basic properties of Fejér monotone mappings, Rostock. Math. Kolloq. 50 (1997), 71-84. Zbl0905.65068
- [8] D. Schott, About strongly Fejér monotone mappings and their relaxations, Zeitschr. Anal. Anw. 16 (1997), 709-726. Zbl0882.65043
- [9] D. Schott, Weak convergence of Fejér monotone iterative methods, Rostock. Math. Kolloq. 51 (1997), 83-96. Zbl0890.65055
- [10] D. Schott, Strongly Fejér monotone mappings, Part III: Interval union model for maximal mappings, preprint.
- [11] H. Stark, (ed.), Image recovery: Theory and applications, Academic Press, New York 1987.

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