- Mosco stability of proximal mappings in reflexive Banach spaces Dan Butnariu (dbutnarumath.haifa.ac.il) Elena Resmerita (elena.resmeritaoeaw.ac.at) Abstract: In this paper we establish criteria for the stability of the proximal mapping \textrm{Prox} $_{\varphi }^{f}=(\partial \varphi +\partial f)^{-1}$ associated to the proper lower semicontinuous convex functions $\varphi$ and $f$ on a reflexive Banach space $X.$ We prove that, under certain conditions, if the convex functions $\varphi _{n}$ converge in the sense of Mosco to $\varphi$ and if $\xi _{n}$ converges to $\xi ,$ then \textrm{Prox} $_{\varphi _{n}}^{f}(\xi _{n})$ converges to \textrm{Prox} $_{\varphi }^{f}(\xi ).$ Keywords: Bregman distance, Legendre function, modulus of total convexity, Mosco convergence of a sequence of functions, proximal mapping relative to a convex function, relative projection onto a convex set, uniformly convex function Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: preprint, 2006 Download: [PDF]Entry Submitted: 04/25/2006Entry Accepted: 04/25/2006Entry Last Modified: 04/25/2006Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.