20 papers
Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting
Felipe Atenas, Heinz H. Bauschke, Minh N. Dao +1
In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework,…
Extending Meshulam's result on the boundedness of orbits of relaxed projections onto affine subspaces from finite to infinite-dimensional Hilbert spaces
Heinz H. Bauschke, Tran Thanh Tung
In 1996, Meshulam proved that any sequence generated in Euclidean space by randomly projecting onto affine subspaces drawn from a finite collection stays bounded even if the inters…
On Opial's Lemma
Aleksandr Arakcheev, Heinz H. Bauschke
Opial's Lemma is a fundamental result in the convergence analysis of sequences generated by optimization algorithms in real Hilbert spaces. We introduce the concept of Opial sequen…
On Characterizations of (Almost) Strictly Convex Functions
Heinz H. Bauschke, Honglin Luo, Xianfu Wang
In this paper, we unify and improve existing results on characterizing strict and almost stricty convex functions via subdifferential mapping, Moreau envelope, and proximal mapping…
Finite Termination of a Generalized Perceptron Algorithm
Heinz H. Bauschke, Tran Thanh Tung
Motivated by Ridgway's proof of the perceptron algorithm, we study a simple subgradient method for convex inequality systems in Hilbert space. Assuming strict feasibility and bound…
Boţ-Nguyen Acceleration, Weighted Mean Ergodic Iteration, and the Beta-Binomial Distribution
Heinz H. Bauschke, Yuan Gao
In 2023, Boţ and Nguyen introduced a new class of accelerated algorithms for finding a fixed point of a nonexpansive operator as the weak limit of a sequence. In this paper, we ana…