On polyhedral and second-order cone decompositions of semidefinite optimization problems
Author(s)Bertsimas, Dimitris J; Cory-Wright, Ryan
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We study a cutting-plane method for semidefinite optimization problems, 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 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.
DepartmentSloan School of Management; Massachusetts Institute of Technology. Operations Research Center
Operations Research Letters
Bertsimas, Dimitris and Ryan Cory-Wright. "On polyhedral and second-order cone decompositions of semidefinite optimization problems." Operations Research Letters 48, 1 (January 2020): 78-85
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