We propose a new primal-dual interior-point algorithm for semidefinite optimization(SDO) based on an eligible barrier function. New search directions and proximity measures are proposed based on the barrier function. We show that the algorithm has Ο(n log(n/ε)) and Ο(√n(log n)log(n/ε)) complexity results for small- and large-update methods, respectively. These are the best known complexity results for such methods.
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