Ball intersection model for Fejér zones of convex closed sets

• Autorzy: Dieter Schott
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

set-valued mappings; Fejér monotone mappings; relaxations; central stretching; convex sets; ball intersections

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 47H04: Set-valued operators
• 65J05: General theory

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 51-79

Daty

wydano

2001

otrzymano

2000-02-20

Twórcy

autor

Dieter Schott

• Electrotechnics and Computer Science College, Wismar, Philipp-Müller-Str. PF 1210, D-23952 Wismar, Germany

Bibliografia

• [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.
• [5] D. Schott, Iterative solution of convex problems by Fejér monotone methods, Numer. Funct. Anal. Optimiz. 16 (1995), 1323-1357.
• [6] D. Schott, Basic properties of Fejér monotone sequences, Rostock. Math. Kolloq. 49 (1995), 57-74.
• [7] D. Schott, Basic properties of Fejér monotone mappings, Rostock. Math. Kolloq. 50 (1997), 71-84.
• [8] D. Schott, About strongly Fejér monotone mappings and their relaxations, Zeitschr. Anal. Anw. 16 (1997), 709-726.
• [9] D. Schott, Weak convergence of Fejér monotone iterative methods, Rostock. Math. Kolloq. 51 (1997), 83-96.
• [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.

Identyfikatory

DOI

10.7151/dmgt.1017