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 500 × 500 matrices.
Citation
@techreport{bertsimas2019polyhedral, title={On Polyhedral and Second-Order-Cone Decompositions of Semidefinite Optimization Problems}, author={Bertsimas, Dimitris and Cory-Wright, Ryan}, institution={Massachusetts Institute of Technology}, year={2019} }