# On Polyhedral and Second-Order Cone Decompositions of Semidefinite Optimization Problems

arXiv: https://arxiv.org/abs/1910.03143 · HTML: https://mlsanity.com/paper/1910.03143/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2019.

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

- [Sparse PCA With Multiple Components](https://mlsanity.com/paper/2209.14790/) (2022)

## Abstract (arXiv)

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 1000s of covariates, and solve nuclear norm problems over 500x500 matrices.