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pro vyhledávání: '"Bauschke, A"'
Autor:
Bauschke, Heinz H., Gao, Yuan
It is well known that the iterates of an averaged nonexpansive mapping may only converge weakly to fixed point. A celebrated result by Baillon, Bruck, and Reich from 1978 yields strong convergence in the presence of linearity. In this paper, we exten
Externí odkaz:
http://arxiv.org/abs/2404.04402
Monotone inclusion problems occur in many areas of optimization and variational analysis. Splitting methods, which utilize resolvents or proximal mappings of the underlying operators, are often applied to solve these problems. In 2022, Bredies, Chenc
Externí odkaz:
http://arxiv.org/abs/2307.09747
Projection operators are fundamental algorithmic operators in Analysis and Optimization. It is well known that these operators are firmly nonexpansive; however, their composition is generally only averaged and no longer firmly nonexpansive. In this n
Externí odkaz:
http://arxiv.org/abs/2303.13738
The solution of the cubic equation has a century-long history; however, the usual presentation is geared towards applications in algebra and is somewhat inconvenient to use in optimization where frequently the main interest lies in real roots. In thi
Externí odkaz:
http://arxiv.org/abs/2302.10731
The Fenchel-Young inequality is fundamental in Convex Analysis and Optimization. It states that the difference between certain function values of two vectors and their inner product is nonnegative. Recently, Carlier introduced a very nice sharpening
Externí odkaz:
http://arxiv.org/abs/2206.14872
Let $A$ be a closed affine subspace and let $B$ be a hyperplane in a Hilbert space. Suppose we are given their associated nearest point mappings $P_A$ and $P_B$, respectively. We present a formula for the projection onto their intersection $A\cap B$.
Externí odkaz:
http://arxiv.org/abs/2206.11373
Publikováno v:
Applied Set-Valued Analysis and Optimization 5 (2023), No. 2, pp. 163-180
In $\mathbb{R}^3$, a hyperbolic paraboloid is a classical saddle-shaped quadric surface. Recently, Elser has modeled problems arising in Deep Learning using rectangular hyperbolic paraboloids in $\mathbb{R}^n$. Motivated by his work, we provide a rig
Externí odkaz:
http://arxiv.org/abs/2206.04878
Let $C$ be a closed convex subset of a real Hilbert space containing the origin, and assume that $K$ is the homogenization cone of $C$, i.e., the smallest closed convex cone containing $C \times \{1\}$. Homogenization cones play an important role in
Externí odkaz:
http://arxiv.org/abs/2206.02694
Autor:
Tekbaş, Aysun, Schilling, Kristina, Fahrner, René, Morath, Olga, Malessa, Christina, Bauschke, Astrid, Settmacher, Utz, Rauchfuß, Falk
Publikováno v:
In Transplantation Proceedings October 2024 56(8):1759-1765
Finding a zero of a sum of maximally monotone operators is a fundamental problem in modern optimization and nonsmooth analysis. Assuming that the resolvents of the operators are available, this problem can be tackled with the Douglas-Rachford algorit
Externí odkaz:
http://arxiv.org/abs/2203.03832