48 citations · 199 across the 83 of their papers we have counts for
38 papers · 1 filter
Roots of the identity operator and proximal mappings: (classical and phantom) cycles and gap vectors
Heinz H. Bauschke, Xianfu Wang
Recently, Simons provided a lemma for a support function of a closed convex set in a general Hilbert space and used it to prove the geometry conjecture on cycles of projections. In…
On angles between convex cones
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
There are two basic angles associated with a pair of linear subspaces: the Diximier angle and the Friedrichs angle. The Dixmier angle of the pair of orthogonal complements is the s…
Resolvents and Yosida approximations of displacement mappings of isometries
Salihah Alwadani, Heinz H. Bauschke, Julian P. Revalski +1
Maximally monotone operators are fundamental objects in modern optimization. The main classes of monotone operators are subdifferential operators and matrices with a positive semid…
Fixed points of compositions of nonexpansive mappings: finitely many linear reflectors
Salihah Alwadani, Heinz H. Bauschke, Xianfu Wang
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point pr…
Proximal mappings and Moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions
Chayne Planiden, Xianfu Wang
This work presents a collection of useful properties of the Moreau envelope for finite-dimensional, proper, lower semicontinuous, convex functions. In particular, gauge functions a…
Epiconvergence, the Moreau envelope and generalized linear-quadratic functions
Chayne Planiden, Xianfu Wang
This work introduces the class of generalized linear-quadratic functions, constructed using maximally monotone symmetric linear relations. Calculus rules and properties of the More…