On Polyhedral and Second-Order Cone Decompositions of Semidefinite Optimization Problems
Optimization and Control
2020-02-17 v2 Machine Learning
Machine Learning
Abstract
We study a cutting-plane method for semidefinite optimization problems (SDOs), and supply a proof of the method's convergence, under a boundedness assumption. By relating the method's rate of convergence to an initial outer approximation's diameter, we argue that the method performs well when initialized with a second-order-cone approximation, instead of a linear approximation. We invoke the method to provide bound gaps of 0.5-6.5% for sparse PCA problems with s of covariates, and solve nuclear norm problems over 500x500 matrices.
Cite
@article{arxiv.1910.03143,
title = {On Polyhedral and Second-Order Cone Decompositions of Semidefinite Optimization Problems},
author = {Dimitris Bertsimas and Ryan Cory-Wright},
journal= {arXiv preprint arXiv:1910.03143},
year = {2020}
}
Comments
Submitted minor revision to Operations Research Letters; removed footnotes and corrected some minor typos in previous version