Zobrazeno 1 - 10
of 292
pro vyhledávání: '"Combettes, Patrick L."'
We propose stochastic algorithms for solving large scale nonsmooth convex composite minimization problems. They activate at each iteration blocks of randomly selected proximity operators and achieve almost sure convergence of the iterates to a soluti
Externí odkaz:
http://arxiv.org/abs/2403.10673
In variational signal processing and machine learning problems, loss functions and linear operators are typically aggregated as an average of composite terms. We propose an alternative formulation using proximal comixtures, an operation that combines
Externí odkaz:
http://arxiv.org/abs/2403.09610
Autor:
Bùi, Minh N., Combettes, Patrick L.
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 monotone operators acting on different spaces and linear operators. As
Externí odkaz:
http://arxiv.org/abs/2311.04790
Autor:
Bùi, Minh N., Combettes, Patrick L.
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 introdu
Externí odkaz:
http://arxiv.org/abs/2311.04117
Autor:
Combettes, Patrick L.
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 typically involves several operators combined through monotonicity-prese
Externí odkaz:
http://arxiv.org/abs/2310.08443
Autor:
Bùi, Minh N., Combettes, Patrick L.
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 underlying space and the integrand are then introduced to convert this princ
Externí odkaz:
http://arxiv.org/abs/2305.04872
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 semicontinuous convex function on the product space. Since perspectiv
Externí odkaz:
http://arxiv.org/abs/2303.05337
The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we investigate
Externí odkaz:
http://arxiv.org/abs/2210.16937
Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent training pr
Externí odkaz:
http://arxiv.org/abs/2210.15064
Autor:
Combettes, Patrick L.
We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the proximal composition, a convexity-preserving operation between a linear operator and a function. The two o
Externí odkaz:
http://arxiv.org/abs/2209.06200