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 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]