Proceedings of the American Mathematical Society

Author(s): T. Pennanen; R. T. Rockafellar; M. Théra
Journal: Proc. Amer. Math. Soc. 130 (2002), 2261-2269.
MSC (2000): Primary 47H05, 78M99
Posted: March 6, 2002
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Abstract: This paper gives sufficient conditions for graphical convergence of sums of maximal monotone mappings. The main result concerns finite-dimensional spaces and it generalizes known convergence results for sums. The proof is based on a duality argument and a new boundedness result for sequences of monotone mappings which is of interest on its own. An application to the epi-convergence theory of convex functions is given. Counterexamples are used to show that the results cannot be directly extended to infinite dimensions.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47H05, 78M99

T. Pennanen
Affiliation: Department of Management Science, Helsinki School of Economics, PL 1210, 00101 Helsinki, Finland
Email: pennanen@hkkk.fi

R. T. Rockafellar
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195-4350
Email: rtr@math.washington.edu

M. Théra
Affiliation: LACO, UPRESSA 6090, Université de Limoges, 123, avenue Albert Thomas, 87060 Limoges Cedex, France
Email: michel.thera@unilim.fr

DOI: 10.1090/S0002-9939-02-06450-X
PII: S 0002-9939(02)06450-X
Keywords: Maximal monotone operators, set-valued mappings, graphical convergence, epiconvergence, subdifferential
Received by editor(s): June 17, 2000
Posted: March 6, 2002
Additional Notes: The first author was supported by the Academy of Finland under grant No. 70468.
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2002, American Mathematical Society

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