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In this paper we propose a primal-dual interior-point algorithm forconvex quadratic semidefinite optimization problem. The searchdirection of algorithm is defined in terms of a matrix function andthe iteration is generated by full-Newton step. Furthermore, wederive the iteration bound for the algorithm with small-updatemethod, namely, O( $\sqrt{n}$ 
log $\frac{n}{\varepsilon}$ 
), which isbest-known bound so far.
