A primal–dual interior point method for nonlinear semidefinite programming
A primal–dual interior point method for nonlinear semidefinite programming
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DOI：
10.1007/s10107-011-0449-z
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发表时间：
2011-03
影响因子：
2.7
通讯作者：
Hiroshi Yamashita;H. Yabe;K. Harada
中科院分区：
文献类型：
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作者：
Hiroshi Yamashita;H. Yabe;K. Harada
研究求解非线性半定规划问题的一种原对偶内点法。该方法由寻找KKT点的外部迭代（SDPIP）和计算近似屏障KKT点的内部迭代（SDPLS）组成。SDPLS算法使用类牛顿方向的交换类来生成线搜索方向。将原障碍惩罚函数与原对偶障碍函数相结合，提出了一种新的原对偶价值函数。证明了该方法的全局收敛性。最后给出了数值实验结果。
This paper is concerned with a primal–dual interior point method for solving nonlinear semidefinite programming problems. The method consists of the outer iteration (SDPIP) that finds a KKT point and the inner iteration (SDPLS) that calculates an approximate barrier KKT point. Algorithm SDPLS uses a commutative class of Newton-like directions for the generation of line search directions. By combining the primal barrier penalty function and the primal–dual barrier function, a new primal–dual merit function is proposed. We prove the global convergence property of our method. Finally some numerical experiments are given.