https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:14074 Wed 27 Jul 2022 15:07:29 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:14072 Wed 27 Jul 2022 15:07:06 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:16127 Wed 27 Jul 2022 14:01:20 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:34118 Wed 04 Sep 2019 09:54:59 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:47673 union averaged nonexpansive. At each point in their domain, the value of such an operator can be expressed as a finite union of single-valued averaged nonexpansive operators. We investigate various structural properties of the class and show, in particular, that is closed under taking unions, convex combinations, and compositions, and that their fixed point iterations are locally convergent around strong fixed points. We then systematically apply our results to analyze proximal algorithms in situations, where union averaged nonexpansive operators naturally arise. In particular, we consider the problem of minimizing the sum two functions, where the first is convex and the second can be expressed as the minimum of finitely many convex functions.]]> Tue 24 Jan 2023 15:55:11 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:47609 Tue 24 Jan 2023 11:14:45 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:40664 Thu 28 Jul 2022 11:42:05 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:42729 Thu 22 Jun 2023 11:58:43 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:14050 Sat 24 Mar 2018 08:22:37 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:18073 Sat 24 Mar 2018 08:06:13 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:27962 Sat 24 Mar 2018 07:38:46 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:27999 Sat 24 Mar 2018 07:38:40 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:27998 gap functions. We propose a very natural gap function for an arbitrary maximal monotone inclusion and will demonstrate how naturally this gap function arises from the Fitzpatrick function, which is a convex function, used to represent maximal monotone operators. This allows us to use the powerful strong Fitzpatrick inequality to analyse solutions of the inclusion. We also study the special cases of a variational inequality and of a generalized variational inequality problem. The associated notion of a scalar gap is also considered in some detail. Corresponding local and global error bounds are also developed for the maximal monotone inclusion.]]> Sat 24 Mar 2018 07:38:40 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:28771 Sat 24 Mar 2018 07:23:45 AEDT ]]>