|
Maximality of sums of two maximal monotone operators in general Banach space
Author(s):
Jonathan
M.
Borwein
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3917-3924.
MSC (2000):
Primary 47H05, 46N10, 46A22
Posted:
September 12, 2007
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
We combine methods from convex analysis, based on a function of Simon Fitzpatrick, with a fine recent idea due to Voisei, to prove maximality of the sum of two maximal monotone operators in Banach space under various natural domain and transversality conditions.
References:
-
- 1.
- BORWEIN, J. M., ``Maximality of sums of two maximal monotone operators,'' Proc. Amer. Math. Soc., 134 (2006), 2951-2956. MR 2231619
- 2.
- BORWEIN, J. M., ``Maximal montonicity via convex analysis,'' Fitzpatrick Memorial Issue of J. Convex Analysis, 13/14 (2006), 561-586.
- 3.
- BORWEIN, J. M. & LEWIS, A. S., Convex Analysis and Nonlinear Optimization: Theory and Examples, Enlarged Edition, Springer-Verlag, New York, 2005. MR 1757448 (2001h:49001)
- 4.
- BORWEIN, J. M. & ZHU, Q. J., Techniques of Variational Analysis: An Introduction, CMS Books, Springer-Verlag, 2005. MR 2144010 (2006h:49002)
- 5.
- BURACHIK, R.S. & SVAITER, B.F., Maximal monotonicity, conjugation and the duality product,'' Proc AMS, 131 (2003), 2379-2383. MR 1974634 (2004a:49037)
- 6.
- FITZPATRICK, S. ``Representing monotone operators by convex functions,'' Workshop/ Miniconference on Functional Analysis and Optimization (Canberra, 1988), 59-65, Proc. Centre Math. Anal. Austral. Nat. Univ., 20, Austral. Nat. Univ., Canberra, 1988. MR 1009594 (90i:47054)
- 7.
- FITZPATRICK, S. & PHELPS, R.R. ``Some properties of maximal monotone operators on nonreflexive Banach spaces,'' Set-valued Analysis, 3 (1995), 51-69. MR 1333366 (96c:47076)
- 8.
- PENOT, J.P., ``The relevance of convex analysis for the study of monotonicity,'' Nonlinear Anal, Theory, Methods, Appl., 58 (2004),855-871. MR 2086060 (2005g:49026)
- 9.
- ROCKAFELLAR, R. T., ``On the maximality of sums of nonlinear monotone operators,'' Trans. Amer. Math. Soc., 149 (1970), 75-88. MR 0282272 (43:7984)
- 10.
- SIMONS, S., Minimax and Monotonicity, Lecture Notes in Mathematics, 1693, Springer-Verlag, Berlin, 1998. MR 1723737 (2001h:49002)
- 11.
- VERONA, A. & VERONA, M. E., ``Regular maximal monotone operators and the sum rule,'' J. Convex Analysis, 7 (2000), 115-128. MR 1773179 (2001h:47087)
- 12.
- VOISEI, M.D., ``A maximality theorem for the sum of maximal monotone operators in non-reflexive Banach Spaces,'' Math. Sci. Res. J., 10 (2) (2006), 36-41. MR 2207807 (2007a:47054)
- 13.
- VOISEI, M.D., ``Calculus rules for maximal monotone operators in general Banach space,'' preprint, 2006.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
47H05, 46N10, 46A22
Retrieve articles in all Journals with MSC
(2000):
47H05, 46N10, 46A22
Additional Information:
Jonathan
M.
Borwein
Affiliation:
Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada
Email:
jborwein@cs.dal.ca
DOI:
10.1090/S0002-9939-07-08960-5
PII:
S 0002-9939(07)08960-5
Keywords:
Maximal monotone operators,
convex analysis,
Fitzpatrick function,
Fenchel duality,
sum theorem
Received by editor(s):
May 3, 2006
Received by editor(s) in revised form:
May 10, 2006 and, September 27, 2006
Posted:
September 12, 2007
Additional Notes:
This author's research was supported by NSERC and by the Canada Research Chair Program.
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org