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arXiv · 1910.03143

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

Dimitris Bertsimas·Ryan Cory-Wright
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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 $1000$s of covariates, and solve nuclear norm problems over 500x500 matrices.

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Dimitris Bertsimas, Ryan Cory-Wright. 2019-12-02. On Polyhedral and Second-Order Cone Decompositions of Semidefinite Optimization Problems. https://doi.org/10.1016/j.orl.2019.12.003

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