48 citations · 76 across the 7 of their papers we have counts for
8 papers · 1 filter
The Resolvent Average for Positive Semidefinite Matrices
Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang
We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interp…
General Resolvents for Monotone Operators: Characterization and Extension
Heinz H. Bauschke, Xianfu Wang, Liangjin Yao
Monotone operators, especially in the form of subdifferential operators, are of basic importance in optimization. It is well known since Minty, Rockafellar, and Bertsekas-Eckstein…
Firmly nonexpansive and Kirszbraun-Valentine extensions: a constructive approach via monotone operator theory
Heinz H. Bauschke, Xianfu Wang
Utilizing our recent proximal-average based results on the constructive extension of monotone operators, we provide a novel approach to the celebrated Kirszbraun-Valentine Theorem…
Monotone Linear Relations: Maximality and Fitzpatrick Functions
Heinz H. Bauschke, Xianfu Wang, Liangjin Yao
We analyze and characterize maximal monotonicity of linear relations (set-valued operators with linear graphs). An important tool in our study are Fitzpatrick functions. The result…
Bregman distances and Klee sets
Heinz H. Bauschke, Xianfu Wang, Jane Ye +1
In 1960, Klee showed that a subset of a Euclidean space must be a singleton provided that each point in the space has a unique farthest point in the set. This classical result has…
Autoconjugate representers for linear monotone operators
Heinz H. Bauschke, Xianfu Wang, Liangjin Yao
Monotone operators are of central importance in modern optimization and nonlinear analysis. Their study has been revolutionized lately, due to the systematic use of the Fitzpatrick…