Graphical convergence of sums of monotone mappings

Pennanen, T.; Rockafellar, R.; Théra, M.

doi:10.1090/S0002-9939-02-06450-X

Graphical convergence of sums of monotone mappings
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by T. Pennanen, R. T. Rockafellar and M. Théra PDF

Proc. Amer. Math. Soc. 130 (2002), 2261-2269 Request permission

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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