- Asymptotic equivalence and Kobayashi-type estimates for nonautonomous monotone operators in Banach spaces F Alvarez (falvarezdim.uchile.cl) J Peypouquet (juan.peypouquetusm.cl) Abstract: We provide a sharp generalization to the nonautonomous case of the well-known Ko\-ba\-yashi estimate for proximal iterates associated with maximal monotone operators. We then derive a bound for the distance between a continuous-in-time trajectory, namely the solution to the differential inclusion $\dot{x} + A(t)x\ni 0$, and the corresponding proximal iterations. We also establish continuity properties with respect to time of the nonautonomous flow under simple assumptions by revealing their link with the function $t\mapsto A(t)$. Moreover, our sharper estimations allow us to derive equivalence results which are useful to compare the asymptotic behavior of the trajectories defined by different evolution systems. We do so by extending a classical result of Passty to the nonautonomous setting. Keywords: Monotone operators, evolution equations, Koayashi-type estimates Category 1: Applications -- Science and Engineering (Basic Sciences Applications ) Citation: Unpublished, UTFSM-CMM, Chile 2008 Download: Entry Submitted: 05/13/2008Entry Accepted: 05/13/2008Entry Last Modified: 04/20/2009Modify/Update this entry Visitors Authors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.