# Limits of maximal monotone operators driven by their representative functions

Limits of maximal monotone operators driven by their representative functions In a previous paper, the authors showed that in a reflexive Banach space the lower limit of a sequence of maximal monotone operators is always representable by a convex function. The present paper gives precisions to the latter result by demonstrating the continuity of the representation with respect to the epi-convergence of the representative functions, and the stability of the class of maximal monotone operators with respect to the Mosco-convergence of their representative functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Optimization Letters Springer Journals

# Limits of maximal monotone operators driven by their representative functions

, Volume 13 (4) – Jun 5, 2018
9 pages

/lp/springer_journal/limits-of-maximal-monotone-operators-driven-by-their-representative-pDNOAXlXzy
Publisher
Springer Journals
Subject
Mathematics; Optimization; Operations Research/Decision Theory; Computational Intelligence; Numerical and Computational Physics, Simulation
ISSN
1862-4472
eISSN
1862-4480
DOI
10.1007/s11590-018-1279-1
Publisher site
See Article on Publisher Site

### Abstract

In a previous paper, the authors showed that in a reflexive Banach space the lower limit of a sequence of maximal monotone operators is always representable by a convex function. The present paper gives precisions to the latter result by demonstrating the continuity of the representation with respect to the epi-convergence of the representative functions, and the stability of the class of maximal monotone operators with respect to the Mosco-convergence of their representative functions.

### Journal

Published: Jun 5, 2018

### References

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