Asymptotic behavior of quasi-nonexpansive mappings

Studies in Computational Mathematics

Volumn 8, Issue C, 2001, Pages 49-68

  Butnariu, Dan ^a   Reich, Simeon ^b   Zaslavski, Alexander J ^b  

^a UNIVERSITY OF HAIFA   (Israel)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956711891     PISSN: 1570579X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1570-579X(01)80006-9     Document Type: Chapter

References (28)

1. Asplund E. Fréchet differentiability of convex functions. Acta Math. 121 (1968) 31-47
2. Ball J.M., and Nadirashvili N.S. Universal singular sets for one-dimensional variational problems. Calc. Var. 1 (1993) 429-438
3. this volume. Bauschke H.H., and Borwein J.M. Joint and separate convexity of the Bregman distance. Inherently Parallel Algorithms in Feasibility and Optimization and their Applications (2001)
4. Borwein J.M., and Preiss D. A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions. Trans. Amer. Math. Soc. 303 (1987) 517-527
5. Bregman L.M. The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Math. and Math. Phys. 7 (1967) 200-217
6. Bregman L.M., Censor Y., and Reich S. Dykstra's algorithm as the nonlinear extension of Bregman's optimization method. J Convex Analysis 6 (1999) 319-333
7. Butnariu D., Censor Y., and Reich S. Iterative averaging of entropic projections for solving stochastic convex feasibility problems. Computational Optimization and Applications 8 (1997) 21-39
8. Butnariu D., and Iusem A.N. Local moduli of convexity and their application to finding almost common fixed points of measurable families of operators. Recent Developments in Optimization Theory and Nonlinear Analysis, Contemporary Mathematics 204 (1997) 61-91
9. Butnariu D., and Iusem A.N. Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization (2000), Kluwer, Dordrecht
10. Butnariu D., Reich S., and Zaslavski A.J. Generic power convergence of operators in Banach spaces. Numerical Functional Analysis and Optimization 20 (1999) 629-650
11. Preprint. Butnariu D., Reich S., and Zaskavski A.J. Asymptotic behavior of relatively nonexpansive operators in Banach spaces (2000)
12. Censor Y., and Lent A. An iterative row-action method for interval convex programming. J. Optim. Theory Appl. 34 (1981) 321-353
13. Censor Y., and Reich S. Iterations of paracontractions and firmly nonexpansive operators with applications to feasibility and optimization. Optimization 37 (1996) 323-339
14. Censor Y., and Zenios S.A. Parallel Optimization (1997), Oxford, New York
15. De Blasi F.S., and Myjak J. Sur la convergence des approximations successives pour les contractions non linéaires dans un espace de Banach. C. R. Acad. Sci. Paris 283 (1976) 185-187
16. De Blasi F.S., and Myjak J. Generic flows generated by continuous vector fields in Banach spaces. Adv. in Math. 50 (1983) 266-280
17. De Blasi F.S., and Myjak J. On a generalized best approximation problem. J. Approximation Theory 94 (1998) 54-72
18. Deville R., and Revalski J. Porosity of ill-posed problems. Proc. Amer. Math. Soc. 128 (2000) 1117-1124
19. Dontchev A.L., and Zolezzi T. Well-Posed Optimization Problems. Lecture Notes in Math. 1543 (19993), Springer, Berlin
20. Ioffe A.D., and Zaslavski A.J. Variational principles and well-posedness in optimization and calculus of variations. SIAM J. Control Optim. 38 (2000) 566-581
21. Kelley J.L. General Topology (1955), D. Van Nostrand, New York
22. Lebourg G. Generic differentiability of Lipschitzian functions. Trans. Amer. Math. Soc. 256 (1979) 125-144
23. Myjak J. Orlicz type category theorems for functional and differential equations. Dissertationes Math. (Rozprawy Mat.) 206 (1983) 1-81
24. S. Reich, A weak convergence theorem for the alternating method with Bregman distances, Theory and Applications of Nonlinear Operators of Accretive and Monotone Type (A.G. Kartsatos, Editor) (1996) 313-318.
25. Reich S., and Zaslavski A.J. Convergence of generic infinite products of nonexpansive and uniformly continuous operators. Nonlinear Analysis 36 (1999) 1049-1065
26. Zaslavski A.J. Turnpike property for extremals of variational problems with vectorvalued functions. Trans. Amer. Math. Soc. 351 (1999) 211-231
27. Zaslavski A.J. Existence of solutions of optimal control problems for a generic integrand without convexity assumptions. Nonlinear Analysis 43 (2001) 339-361
28. A.J. Zaslavski, Generic well-posedness of optimal control problems without convexityassumptions, SIAM J. Control Optim., in press.