On polyhedral and second-order cone decompositions of semidefinite optimization problems
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 ini...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Elsevier BV
2021
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| Online Access: | https://hdl.handle.net/1721.1/129965 |
| Summary: | 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. |
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