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

10/08/2019 ∙ by Dimitris Bertsimas, et al. ∙ 0

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

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