Graphical convergence of sums of monotone mappings
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- by T. Pennanen, R. T. Rockafellar and M. Théra PDF
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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.References
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Additional Information
- 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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2261-2269
- MSC (2000): Primary 47H05, 78M99
- DOI: https://doi.org/10.1090/S0002-9939-02-06450-X
- MathSciNet review: 1896407