# A flexible coordinate descent method

@article{Fountoulakis2018AFC, title={A flexible coordinate descent method}, author={Kimon Fountoulakis and Rachael Tappenden}, journal={Computational Optimization and Applications}, year={2018}, volume={70}, pages={351-394} }

We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Flexible Coordinate Descent (FCD). At each iteration of FCD, a block of coordinates is sampled randomly, a quadratic model is formed about that block and the model…

## 18 Citations

### Inexact Variable Metric Stochastic Block-Coordinate Descent for Regularized Optimization

- Mathematics, Computer ScienceJ. Optim. Theory Appl.
- 2020

The analysis generalizes, to the regularized case, Nesterov’s proposal for improving convergence of block-coordinate descent by sampling proportional to the blockwise Lipschitz constants, and improves the convergence rate in the convex case by weakening the dependency on the initial objective value.

### SONIA: A Symmetric Blockwise Truncated Optimization Algorithm

- Computer ScienceAISTATS
- 2021

Theoretical results are presented to confirm that the algorithm converges to a stationary point in both the strongly convex and nonconvex cases, and a stochastic variant of the algorithm is also presented, along with corresponding theoretical guarantees.

### Greed is good : greedy optimization methods for large-scale structured problems

- Computer Science
- 2018

This dissertation shows that greedy coordinate descent and Kaczmarz methods have efficient implementations and can be faster than their randomized counterparts for certain common problem structures in machine learning, and shows linear convergence for greedy (block) coordinate descent methods under a revived relaxation of strong convexity from 1963.

### Newton-Laplace Updates for Block Coordinate Descent

- Computer Science
- 2019

Nutini et al. show that when the chosen block’s sparsity pattern has a tree structure, “message-passing” algorithms can be used to solve the system in linear time and exploit the width of the Hessian's computation graph to speed up the Newton update.

### Fast and Safe: Accelerated Gradient Methods With Optimality Certificates And Underestimate Sequences

- Computer Science, Mathematics
- 2021

This work introduces the concept of an Underestimate Sequence (UES), which is motivated by Nesterov’s estimate sequence, and proposes several first order methods for minimizing strongly convex functions in both the smooth and composite cases.

### Globalized inexact proximal Newton-type methods for nonconvex composite functions

- Mathematics, Computer ScienceComput. Optim. Appl.
- 2021

This work presents a globalized proximal Newton-type method which allows the smooth term to be nonconvex, and some numerical results indicate that this method is very promising also from a practical point of view.

### Let's Make Block Coordinate Descent Go Fast: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence

- Computer Science
- 2017

This paper proposes new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule and considers optimal active manifold identification, which leads to bounds on the "active set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions.

### Let's Make Block Coordinate Descent Converge Faster: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence

- Computer Science
- 2017

This paper proposes new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule and considers optimal active manifold identification, which leads to bounds on the “active-set complexity” of BCD methods and leads to superlinear convergence for certain problems with sparse solutions.

### Graphical Newton for Huge-Block Coordinate Descent on Sparse Graphs

- Computer Science, Mathematics
- 2017

This paper shows how to use message-passing to compute the Newton step in O(|b|) when the block has a forest-structured dependency, allowing us to update huge blocks for sparse problems, resulting in significant numerical improvements over existing approaches.

### Second order semi-smooth Proximal Newton methods in Hilbert spaces

- Mathematics, Computer ScienceComput. Optim. Appl.
- 2022

We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose less restrictive assumptions on the composite…

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