462. Hilbert direct integrals of monotone operators
Invited abstract in session MC-9: Generalized convexity and monotonicity 2, stream Generalized convexity and monotonicity.
Monday, 14:00-16:00Room: B100/8013
Authors (first author is the speaker)
| 1. | Nhut Minh Bui
|
| Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz |
Abstract
Finite Cartesian products of operators play a central role in monotone operator theory and its applications. Extending such products to arbitrary families of operators acting on different Hilbert spaces is an open problem, which we address by introducing the Hilbert direct integral of a family of monotone operators. We present properties of this construct, as well as conditions under which the direct integral inherits the properties of the factor operators. Applications to monotone inclusion and variational problems are discussed. Joint work with Patrick Combettes.
Keywords
- Monotone inclusion problems
- Non-smooth optimization
- Stochastic optimization
Status: accepted
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