Optim Lett https://doi.org/10.1007/s11590-018-1279-1 ORIGINAL PAPER Limits of maximal monotone operators driven by their representative functions 1 2,3 Yboon García · Marc Lassonde Received: 3 January 2018 / Accepted: 29 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 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 demon- strating 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. Keywords Maximal monotone operator · Convex function · Representative function · Epi-convergence · Mosco-convergence · Subdifferential 1 Introduction Let X be a real Banach space. We denote by X its topological dual and by ., . the duality product in X × X , that is, ∗ ∗ x , x := x (x ). The product space X × X is assumed to be equipped with the norm topology. When- ∗∗ ∗ ever necessary, the space X is considered as a subspace
Optimization Letters – Springer Journals
Published: Jun 5, 2018
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