On the Convergence of Alternating Minimization for Convex Programming with Applications to Iteratively Reweighted Least Squares and Decomposition Schemes

By Amir Beck. 2015

238 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Thomas Pock
2. Antonin Chambolle
3. Francis R. Bach
4. G. Peyr'e
5. Lénaïc Chizat
6. Bernhard Schmitzer
7. Shoham Sabach
8. J. Langford

In Computational Theory and Mathematics

1. Antonin Chambolle
2. Thomas Pock
3. G. Peyr'e
4. Lénaïc Chizat
5. Suleyman Serdar Kozat
6. Tolga Ergen
7. Bernhard Schmitzer
8. Alekh Agarwal

In Numerical Analysis

1. Thomas Pock
2. Antonin Chambolle
3. Alekh Agarwal
4. G. Peyr'e
5. Shoham Sabach
6. Lénaïc Chizat
7. Suleyman Serdar Kozat
8. Tolga Ergen

Citations in the corpus

• Robust Aggregation for Federated Learning (2019, neutral): “Comparison to Beck [6].”
• The Cyclic Block Conditional Gradient Method for Convex Optimization Problems (2015, background): “, [6, 2]), which is always a quantity smaller than LF .”
• An introduction to continuous optimization for imaging (2016, methodology): “We should mention here that Becker and Fadili (2012) have shown that, in problems with separable simple functions, one can in fact use preconditioners that are diagonal+rank one, without altering the simplicity of the functions.”
• Unsupervised Anomaly Detection With LSTM Neural Networks (2017, methodology): “, the learning rate, in most of real-life applications [32].”
• Scaling Algorithms for Unbalanced Transport Problems (2016, background): “Moreover (minus) the dual functional has the structure Lipschitz on the sublevel sets of I and (ii) I admits minimizers, so that [6, Thm. 3.9] applies and proves In order to check (i), take any feasible point s for F .”
• Federated Residual Learning (2020, methodology): “Next, we state a lemma that is useful for showing the convergence of alternating minimization, which is adapted from the analysis in (Beck, 2015).”
• Stochastic Joint Radio and Computational Resource Management for Multi-User Mobile-Edge Computing Systems (2017, methodology): “Remark 3: The proposed Gauss-Seidel method updates the transmit powe r and bandwidth allocation alternately in each iteration, which will conve rg to the optimal solution of SP2 with a sublinear convergence rate [40].”