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Graphical convergence of sums of monotone mappings

Authors: T. Pennanen, R. T. Rockafellar and M. Théra
Journal: Proc. Amer. Math. Soc. 130 (2002), 2261-2269
MSC (2000): Primary 47H05, 78M99
Published electronically: March 6, 2002
MathSciNet review: 1896407
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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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Additional Information

T. Pennanen
Affiliation: Department of Management Science, Helsinki School of Economics, PL 1210, 00101 Helsinki, Finland

R. T. Rockafellar
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195-4350

M. Théra
Affiliation: LACO, UPRESSA 6090, Université de Limoges, 123, avenue Albert Thomas, 87060 Limoges Cedex, France

Keywords: Maximal monotone operators, set-valued mappings, graphical convergence, epiconvergence, subdifferential
Received by editor(s): June 17, 2000
Published electronically: March 6, 2002
Additional Notes: The first author was supported by the Academy of Finland under grant No. 70468.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society