4 papers
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 a result by Meshulam
Heinz H. Bauschke, Tran Thanh Tung
In 1996, Meshulam proved that every sequence generated by applying projections onto affine subspaces, drawn from a finite collection in Euclidean space, must be bounded. In this pa…
The Güntürk-Thao theorem revisited: polyhedral cones and limiting examples
Heinz H. Bauschke, Tran Thanh Tung
In 2023, Güntürk and Thao proved that the sequence generated by random (relaxed) projections drawn from a finite collection of innately regular close…
On the boundedness of the sequence generated by minibatch stochastic gradient descent
Heinz H. Bauschke, Tran Thanh Tung
Stochastic Gradient Descent (SGD) with Polyak's stepsize has recently gained renewed attention in stochastic optimization. Recently, Orvieto, Lacoste-Julien, and Loizou introduced…