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本文提出求解二次半定规划的一个基于 H..K..M方向的原始对偶路径跟踪算法.文中首先导出确定H..K..M方向的线性方程组，并证明该搜索方向的存在唯一性；然后给出算法的具体步骤，并证明算法产生的迭代点列落在中心路径的某个邻域内.最后采用 Matlab(R2011b)数学软件编程对算法进行数值试验.数值结果表明算法是有效的.“,”A primal-dual path-following algorithm based on H..K..M direction for quadratic semi-definite programming problems(QSDP)is proposed.Firstly,the system of linear equa-tions yielding the H..K..M direction are derived,and the existence and uniqueness of the search direction are shown;Secondly,the algorithm is described in detail.We show that the it-erates generated by the algorithm can fall into some neighborhood of the central path under some mild conditions.Finally,a preliminary numerical experiment is performed for the algo-rithm by using Matlab (R2011b)mathematical software,and the numerical results show that the proposed algorithm is effective.