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On the maximality of sums of nonlinear monotone operators
Open accessAbstract
R. T. ROCKAFELLAR(')= {*?+x% I xf e Tx(x), xt e T2(x)}.If Tx and F2 are maximal, it does not necessarily follow, however, that F», + T2 is maximal-some sort of condition is needed, since for example the graph of Tx + T2 can even be empty (as happens when D(Tx) n D(T2)= 0).The problem of determining conditions under which Tx + T2 is maximal turns out to be of fundamental importance in the theory of monotone operators.Results in this direction have been proved by Lescarret [9] and Browder [5], [6], [7].The strongest result which is known at present is : Theorem (Browder [6],[7]).Let X be reflexive, and let Tx and T2 be monotone operators from X to X*. Suppose that Tx is maximal, D(T2) = X, T2 is single-valued
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Cited by
Parikh, N., & Boyd, S. (2014) · Foundations and Trends® in Optimization · doi:10.1561/2400000003 · Cited by 4,102
Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming
Eckstein, J. (1993) · Mathematics of Operations Research · doi:10.1287/moor.18.1.202 · Cited by 324
Metadata
- Authors
- Rockafellar, R. T.
- Venue
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 1970
- Volume
- 149
- Issue
- 1
- Pages
- 75-88
- ISSN
- 0002-9947 (ISSN-L)
- 1088-6850
- OpenAlex
- W2132677982
- Cited by
- 949
- References
- 0
- FWCI
- 8.86
- Type
- journal article
- Language
- en
- Open access
- bronze
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