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1.
Heinz H. Bauschke 《Proceedings of the American Mathematical Society》2007,135(1):135-139
Recently, S. Reich and S. Simons provided a novel proof of the Kirszbraun-Valentine extension theorem using Fenchel duality and Fitzpatrick functions. In the same spirit, we provide a new proof of an extension result for firmly nonexpansive mappings with an optimally localized range.
2.
Heinz H. Bauschke Patrick L. Combettes 《Proceedings of the American Mathematical Society》2003,131(12):3757-3766
An iterative method is proposed to construct the Bregman projection of a point onto a countable intersection of closed convex sets in a reflexive Banach space.
3.
Maximally monotone operators and firmly nonexpansive mappings play key roles in modern optimization and nonlinear analysis. Five years ago, it was shown that if finitely many firmly nonexpansive operators are all asymptotically regular (i.e., they have or “almost have” fixed points), then the same is true for compositions and convex combinations. In this paper, we derive bounds on the magnitude of the minimal displacement vectors of compositions and of convex combinations in terms of the displacement vectors of the underlying operators. Our results completely generalize earlier works. Moreover, we present various examples illustrating that our bounds are sharp. 相似文献
4.
Abstract The Chlorophosphatebetaine (I), synthesized 1981 by Meisel and Wolf (1), was applied in one-bottle approach for synthesis of nucleoside di- and triphosphates or dinucleotides in μmol-scale with good yields (2). 相似文献
5.
Alwadani Salihah Bauschke Heinz H. Revalski Julian P. Wang Xianfu 《Set-Valued and Variational Analysis》2021,29(3):721-733
Set-Valued and Variational Analysis - Maximally monotone operators are fundamental objects in modern optimization. The main classes of monotone operators are subdifferential operators and matrices... 相似文献
6.
Heinz H. Bauschke Graeme R. Douglas Walaa M. Moursi 《Journal of Fixed Point Theory and Applications》2016,18(2):297-307
In 1971, Pazy [Israel J. Math. 9 (1971), 235–240] presented a beautiful trichotomy result concerning the asymptotic behaviour of the iterates of a nonexpansive mapping. In this note, we analyze the fixedpoint- free case in more detail. Our results and examples give credence to the conjecture that the iterates always converge cosmically. The relationship to recent work by Lins [Proc. Amer. Math. Soc. 137 (2009), 2387–2392] is also discussed. 相似文献
7.
Heinz H. Bauschke Frank Deutsch Hein Hundal Sung-Ho Park 《Transactions of the American Mathematical Society》2003,355(9):3433-3461
The powerful von Neumann-Halperin method of alternating projections (MAP) is an algorithm for determining the best approximation to any given point in a Hilbert space from the intersection of a finite number of subspaces. It achieves this by reducing the problem to an iterative scheme which involves only computing best approximations from the individual subspaces which make up the intersection. The main practical drawback of this algorithm, at least for some applications, is that the method is slowly convergent. In this paper, we consider a general class of iterative methods which includes the MAP as a special case. For such methods, we study an ``accelerated' version of this algorithm that was considered earlier by Gubin, Polyak, and Raik (1967) and by Gearhart and Koshy (1989). We show that the accelerated algorithm converges faster than the MAP in the case of two subspaces, but is, in general, not faster than the MAP for more than two subspaces! However, for a ``symmetric' version of the MAP, the accelerated algorithm always converges faster for any number of subspaces. Our proof seems to require the use of the Spectral Theorem for selfadjoint mappings.
8.
Mathematical Programming - The notion of best approximation mapping (BAM) with respect to a closed affine subspace in finite-dimensional spaces was introduced by Behling, Bello Cruz and Santos to... 相似文献
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Numerical Algorithms - The circumcentered Douglas–Rachford method (C–DRM), introduced by Behling, Bello Cruz and Santos, iterates by taking the circumcenter of associated successive... 相似文献
10.
We discuss the Douglas–Rachford algorithm to solve the feasibility problem for two closed sets A,B in \({\mathbb{R}^d}\) . We prove its local convergence to a fixed point when A,B are finite unions of convex sets. We also show that for more general nonconvex sets the scheme may fail to converge and start to cycle, and may then even fail to solve the feasibility problem. 相似文献