论文标题
使用Monteiro-tsuchiya搜索方向的非线性半决赛优化的原始双偶内点方法的局部收敛
Local convergence of primal-dual interior point methods for nonlinear semidefinite optimization using the Monteiro-Tsuchiya family of search directions
论文作者
论文摘要
非线性半明确优化问题（称为NSDPS）的最新算法的最新进展是显着的。 Yamashita等。首先提出了使用Monteiro-Zhang（MZ）搜索方向的家族来解决NSDP的原始双重内部点法（PDIPM）。从那时起，就已经提出了针对NSDP的各种pdipms，但据我们所知，它们都是基于MZ家族的。在本文中，我们提出了一个配备了Monteiro-Tsuchiya（MT）方向的PDIPM，该PDIPM最初是为了解决线性半明确优化问题而设计的，就像MZ家族一样。我们进一步证明，在某些对缩放矩阵的一般假设的存在下，NSDP的Karush-Kuhn-tucker点局部局部超线性收敛，这些假设用于生成MT缩放方向。
The recent advance of algorithms for nonlinear semi-definite optimization problems, called NSDPs, is remarkable. Yamashita et al. first proposed a primal-dual interior point method (PDIPM) for solving NSDPs using the family of Monteiro-Zhang (MZ) search directions. Since then, various kinds of PDIPMs have been proposed for NSDPs, but, as far as we know, all of them are based on the MZ family. In this paper, we present a PDIPM equipped with the family of Monteiro-Tsuchiya (MT) directions, which were originally devised for solving linear semi-definite optimization problems as were the MZ family. We further prove local superlinear convergence to a Karush-Kuhn-Tucker point of the NSDP in the presence of certain general assumptions on scaling matrices, which are used in producing the MT scaling directions.
