Abstract
We propose a primal-dual interior-point algorithm for semidefinite optimization(SDO) based on a class of kernel functions which are both eligible and self-regular. New search direc- tions and proximity measures are defined based on these functions. We show that the algorithm has O( √ nlog n ) and O( √ nlognlog n ) complexity results for small- and large-update meth- ods, respectively. These are the best known complexity results for such methods. This is the first algorithm for SDO based on this kernel function, as far as we know.
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