5 papers
Bregman circumcenters: basic theory
Hui Ouyang, Xianfu Wang
Circumcenters play an important role in the design and analysis of accelerating various iterative methods in optimization. In this work, we propose Bregman (pseudo-)circumcenters a…
Best approximation mappings in Hilbert spaces
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
The notion of best approximation mapping (BAM) with respect to a closed affine subspace in finite-dimensional space was introduced by Behling, Bello Cruz and Santos to show the lin…
On the linear convergence of circumcentered isometry methods
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
The circumcentered Douglas--Rachford method (C--DRM), introduced by Behling, Bello Cruz and Santos, is an acceleration of the well-known Douglas-Rachford method (DRM) for finding t…
Circumcentered methods induced by isometries
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
Motivated by the circumcentered Douglas--Rachford method recently introduced by Behling, Bello Cruz and Santos to accelerate the Douglas--Rachford method, we study the properness o…
On circumcenter mappings induced by nonexpansive operators
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
We introduce the circumcenter mapping induced by a set of (usually nonexpansive) operators. One prominent example of a circumcenter mapping is the celebrated Douglas--Rachford spli…