On the Identification of the Optimal Partition of Second Order Cone Optimization Problems

On the Identification of the Optimal Partition of Second Order Cone Optimization Problems

This paper discusses the identification of the optimal partition of second order cone optimization (SOCO). By giving some condition numbers which only depend on the SOCO problem itself, we derive some bounds on the magnitude of the blocks of variables along the central path and prove that the optima...

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Bibliographic Details
Published in:SIAM journal on optimization 2014-01, Vol.24 (1), p.385-414
Main Authors: Terlaky, Tamas, Wang, Zhouhong
Format: Article
Language:eng
Subjects:
Applied mathematics
Barriers
Optimization
Partitions
Variables
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Summary:This paper discusses the identification of the optimal partition of second order cone optimization (SOCO). By giving some condition numbers which only depend on the SOCO problem itself, we derive some bounds on the magnitude of the blocks of variables along the central path and prove that the optimal partition $\mathcal{B}, \mathcal{N}, \mathcal{R}$, and $\mathcal{T}$ for SOCO problems can be identified along the central path when the barrier parameter $\mu$ is small enough. Then we generalize the results to a specific neighborhood of the central path. [PUBLICATION ABSTRACT]
ISSN:1052-6234
1095-7189