中文摘要：

选择合适的核函数对设计求解线性规划与半正定规划的原始对偶内点算法以及复杂性分析都十分重要.Bai等针对线性规划提出三种核函数,并给出求解线性规划的大步迭代复杂界,但未给出数值算例验证算法的实际效果（Bai Y Q,Xie W,Zhang J.New parameterizedkernel functions for linear optimization.J Global Optim,2012.DOI 10.1007/s10898-012-9934-z）.基于这三种核函数设计了新的求解半正定规划问题的原始对偶内点算法.进一步分析了算法关于大步方法的计算复杂性界,同时通过数值算例验证了算法的有效性和核函数所带参数对计算复杂性的影响.

英文摘要：

It is well known that the choice of a suitable kernel function plays an important role in both theoretical analysis and practical performance of interior- point algorithms for linear and semidefinite programming problems. We are moti- vated by the three kernel functions and the corresponding primal-dual interior-point algorithm for linear programming which were originally proposed by Bai, et al. （Bai Y Q, Xie W, Zhang J. New parameterized kernel functions for linear optimization. J Global Optim, 2012. DOI 10.1007/s10898-012-9934-z）. In this paper, based on the three kernel functions, we propose a new primal-dual interior-point algorithm for semidefinite programming. We first derive the complexity bound of the pro- posed algorithm for large-update methods. Then, we report the numerical tests of the computational performance of the proposed algorithm and the effects of the parameters in the kernel functions.