Ball intersection model for Fejér zones of convex closed sets

Dieter Schott

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

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

Abstract

top
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.

How to cite

top

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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.