Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Combettes, Patrick L."'
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:
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
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
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
Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be represented using
Externí odkaz:
http://arxiv.org/abs/2101.04074
Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving operators th
Externí odkaz:
http://arxiv.org/abs/2005.10235
Autor:
Combettes, Patrick L.
Many functions encountered in applied mathematics and in statistical data analysis can be expressed in terms of perspective functions. One of the earliest examples is the Fisher information, which appeared in statistics in the 1920s. We analyze vario
Externí odkaz:
http://arxiv.org/abs/1610.01552
Autor:
Combettes, Patrick L., Dũng, Dinh
Let $P(D)$ be the differential operator induced by a polynomial $P$, and let ${U^{[P]}_2}$ be the class of multivariate periodic functions $f$ such that $\|P(D)(f)\|_2\leq 1$. The problem of computing the asymptotic order of the Kolmogorov $n$-width
Externí odkaz:
http://arxiv.org/abs/1412.6400
Autor:
Combettes, Patrick L., Yamada, Isao
Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting algorithm for find
Externí odkaz:
http://arxiv.org/abs/1407.5100