A New Notion of Weighted Centers for Semidefinite Programming
A New Notion of Weighted Centers for Semidefinite Programming
复制标题
半定规划加权中心的新概念
DOI：
10.1137/040613378
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Chek Beng Chua
中科院分区：
文献类型：
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作者：
Chek Beng Chua
加权中心的概念在线性规划的V-空间邻域点算法中是必不可少的。虽然有一些成功的推广这一概念的半定规划通过加权中心方程，我们仍然没有一个推广，保持两个重要的性质-（1）每一个选择的权重唯一地确定一对原始-对偶加权中心，（2）所有原始-对偶加权中心的集合完全填补了原始-对偶可行域的相对内部。本文提出了半定规划权中心的一个新概念，它同时具有唯一性和完备性。进一步证明了在严格互补条件下，这些加权中心收敛于最优面的加权中心。最后，将这一收敛结果应用于齐次锥规划，证明了齐次锥规划的一类最优障碍所定义的中心路径在存在严格互补解的情况下收敛于最优面的解析中心.
The notion of weighted centers is essential in V-space interior-point algorithms for linear programming. Although there were some successes in generalizing this notion to semidefinite programming via weighted center equations, we still do not have a generalization that preserves two important properties---(1) each choice of weights uniquely determines a pair of primal-dual weighted centers, and (2) the set of all primal-dual weighted centers completely fills up the relative interior of the primal-dual feasible region. This paper presents a new notion of weighted centers for semidefinite programming that possesses both uniqueness and completeness. Furthermore, it is shown that under strict complementarity, these weighted centers converge to weighted centers of optimal faces. Finally, this convergence result is applied to homogeneous cone programming, where the central paths defined by a certain class of optimal barriers for homogeneous cones are shown to converge to analytic centers of optimal faces in the presence of strictly complementary solutions.