ε-Enlargements of Maximal Monotone Operators in Banach Spaces

Set-Valued Analysis

Volumn 7, Issue 2, 1999, Pages 117-132

  Burachik, Regina Sandra ^a   Svaiter, B F ^b  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b IMPA   (Brazil)

Author keywords

Banach spaces; Br ndsted Rockafellar property; Enlargement of an operator; Lipschitz continuity; Local boundedness; Maximal monotone operators; Transportation formula

Indexed keywords

EID: 0000229314     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008730230603     Document Type: Article

References (13)

1. Brøndsted, A. and Rockafellar, R. T.: On the subdifferentiability of convex functions, Proc. Amer. Math. Soc. 16 (1965), 605-611.
2. Browder, F. E.: Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math. 18(2) (1968).
3. Burachik, R. S., Iusem, A. N. and Svaiter, B. F.: Enlargements of maximal monotone operators with application to variational inequalities, Set-Valued Anal. 5 (1997), 159-180.
4. Burachik, R. S., Sagastizábal, C. A. and Svaiter, B. F.: ε-enlargement of maximal monotone operators with application to variational inequalities, in: M. Fukushima and L. Qi (eds), Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Kluwer Acad. Publ., Dordrecht, 1997.
5. Burachik, R. S., Sagastizábal, C. A. and Svaiter, B. F.: Bundle methods for maximal monotone operators, in: R. Tichatschke and M. Thera (eds), Ill-Posed Variational Problems and Regularization Techniques, Lecture Notes in Control and Inform. Sci., Springer, New York, 1999 (to appear).
6. Ciorǎnescu, I.: Aplicatii de dualitate in analiza functionalǎ neliniarǎ, Ed. Acad. Bucuresti, 1974.
7. Hiriart-Urruty, J.-B.: Lipschitz r-continuity of the approximate subdifferential of a convex function, Math. Scand. 47 (1980), 123-134.
8. Hiriart-Urruty, J.-B. and Lemaréchal, C.: Convex Analysis and Minimization Algorithms, Grundlehren Math. Wiss. 305-306, Springer, Berlin, 1993. (Two volumes.)
9. Kato, T.: Demicontinuity, hemicontinuity and monotonicity, Bull. Amer. Math. Soc. 70 (1964), 548-550.
10. Lemaréchal, C.: Extensions diverses des méthodes de gradient et applications, Thèse d'Etat, Université de Paris IX, 1980.
11. Rockafellar, R. T.: Local boundedness of nonlinear monotone operators, Michigan Math. J. 16 (1969), 397-407.
12. Rockafellar, R. T.: On the maximal monotonicity of subdifferential mappings, Pacific J. Math. 33 (1970), 209-216.
13. Veselý, L.: Local uniform boundedness principle for families of ε-monotone operators, Nonlinear Anal. 24(9) (1995), 1299-1304.