# On complexity and convergence of high-order coordinate descent algorithms for smooth nonconvex box-constrained minimization

arXiv: https://arxiv.org/abs/2009.01811 · HTML: https://mlsanity.com/paper/2009.01811/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2020.

## Built on by (most cited first, 1 of 1)

- [A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks](https://mlsanity.com/paper/2305.14477/) (2023)

## Abstract (arXiv)

Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models for smooth nonconvex box-constrained minimization are introduced in this work. High-order stationarity asymptotic convergence and first-order stationarity worst-case evaluation complexity bounds are established. The computer work that is necessary for obtaining first-order varepsilon-stationarity with respect to the variables of each coordinate-descent block is O(varepsilon-(p+1)/p) whereas the computer work for getting first-order varepsilon-stationarity with respect to all the variables simultaneously is O(varepsilon-(p+1)). Numerical examples involving multidimensional scaling problems are presented. The numerical performance of the methods is enhanced by means of coordinate-descent strategies for choosing initial points.