21 citations · 44 across the 40 of their papers we have counts for
6 papers · 1 filter
Nearly convex sets: fine properties and domains or ranges of subdifferentials of convex functions
Sarah M. Moffat, Walaa M. Moursi, Xianfu Wang
Nearly convex sets play important roles in convex analysis, optimization and theory of monotone operators. We give a systematic study of nearly convex sets, and construct examples…
On Fejér monotone sequences and nonexpansive mappings
H. H. Bauschke, M. N. Dao, W. M. Moursi
The notion of Fejér monotonicity has proven to be a fruitful concept in fixed point theory and optimization. In this paper, we present new conditions sufficient for convergence of…
The Douglas-Rachford algorithm in the affine-convex case
Heinz H. Bauschke, Minh N. Dao, Walaa M. Moursi
The Douglas-Rachford algorithm is a simple yet effective method for solving convex feasibility problems. However, if the underlying constraints are inconsistent, then the convergen…
On a result of Pazy concerning the asymptotic behaviour of nonexpansive mappings
Heinz H. Bauschke, Graeme R. Douglas, Walaa M. Moursi
In 1971, Pazy presented a beautiful trichotomy result concerning the asymptotic behaviour of the iterates of a nonexpansive mapping. In this note, we analyze the fixed-point free c…
On the order of the operators in the Douglas-Rachford algorithm
Heinz H. Bauschke, Walaa M. Moursi
The Douglas-Rachford algorithm is a popular method for finding zeros of sums of monotone operators. By its definition, the Douglas-Rachford operator is not symmetric with respect t…
The Douglas-Rachford algorithm for two (not necessarily intersecting) affine subspaces
Heinz H. Bauschke, Walaa M. Moursi
The Douglas--Rachford algorithm is a classical and very successful splitting method for finding the zeros of the sums of monotone operators. When the underlying operators are norma…