Natural closures, natural compositions and natural sums of monotone operators |
| |
Authors: | Jean-Paul Penot |
| |
Institution: | Laboratoire de Mathématiques Appliquées, CNRS UMR 5142, Faculté des Sciences, Université de Pau et des Pays de l'Adour, BP 1155, 64013 Pau, France |
| |
Abstract: | We introduce new methods for defining generalized sums of monotone operators and generalized compositions of monotone operators with linear maps. Under asymptotic conditions we show these operations coincide with the usual ones. When the monotone operators are subdifferentials of convex functions, a similar conclusion holds. We compare these generalized operations with previous constructions by Attouch–Baillon–Théra, Revalski–Théra and Pennanen–Revalski–Théra. The constructions we present are motivated by fuzzy calculus rules in nonsmooth analysis. We also introduce a convergence and a closure operation for operators which may be of independent interest. |
| |
Keywords: | MSC: 47H05 |
本文献已被 ScienceDirect 等数据库收录! |
|