4 citations · 13 across the 18 of their papers we have counts for
5 papers · 1 filter
Integral Resolvent and Proximal Mixtures
Minh N. Bùi, Patrick L. Combettes
Using the theory of Hilbert direct integrals, we introduce and study a monotonicity-preserving operation, termed the integral resolvent mixture. It combines arbitrary families of m…
Hilbert Direct Integrals of Monotone Operators
Minh N. Bùi, Patrick L. Combettes
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 di…
The Geometry of Monotone Operator Splitting Methods
Patrick L. Combettes
We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which ty…
Interchange Rules for Integral Functions
Minh N. Bùi, Patrick L. Combettes
We first present an abstract principle for the interchange of infimization and integration over spaces of mappings taking values in topological spaces. New conditions on the underl…
Proximity Operators of Perspective Functions with Nonlinear Scaling
Luis M. Briceño-Arias, Patrick L. Combettes, Francisco J. Silva
A perspective function is a construction which combines a base function defined on a given space with a nonlinear scaling function defined on another space and which yields a lower…