对称锥上基于宽邻域的预估矫正算法

A mehrotra-type predictor-corrector algorithm based on wide neighborhood for symmetric programming

在对称锥上提出了一种新的Mehrotra型预估矫正算法,每部迭代都跟踪宽领域N-∞(τ),但不一定属于该邻域,但是总在更宽的邻域N(τ,β),我们给出了比原邻域更好的复杂性O(n(1/2)L),在对称锥规划上,它具有路径跟踪算法最好的复杂性.

In this article we propose a new Mehrotra-type predictor-corrector interior point algorithm for symmetric cone programming. Each iteration always follows the usual wide neighborhood N-∞ （τ）. Even though the iteration does not al- ways stay within this neighborhood, it must stay within a wider neighborhood N（τ ,β）. It shows that the algorithm has iteration complexity O（√nL）, which is better than that of the usual wide neighborhood, and O（√nL） has the best result in regard to the iteration complexity in the context of path-following method for symmetric cone programming.