Limits of maximal monotone operators driven by their representative functions

2017/12/24 by Garcia, Yboon, Lassonde, Marc
#47H05 (Primary) #47N10 (Secondary) #49J52 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1712.08931

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.

Related

• Limits of sequences of maximal monotone operators
• Representation formulas for maximal monotone operators of type (D) in Banach spaces whose dual spaces are strictly convex
• Faces and Support Functions for the Values of Maximal Monotone Operators
• Maximal monotonicity, conjugation and the duality product in non-reflexive Banach spaces
• Recent progress on Monotone Operator Theory