对称锥规划的邻域跟踪算法
摘要
The neighborhood-following algorithm of linear programming, developed by Ai, is extended to symmetric cones. We define a new wide neighborhood <italic>N</italic>(<italic>τ</italic>, <italic>β</italic>) and prove a key property which plays a crucial role in the complexity analysis. Staring with an initial point in <italic>N</italic>(<italic>τ</italic>, <italic>β</italic>), the complexity bound is <italic>O</italic>(√<italic>r</italic> log<italic>ε</italic><sup>-1</sup>) for the Nesterov-Todd (NT) direction, where r is the rank of the associated Euclidean Jordan algebra and <italic>ε</italic>>0 is the required precision. Then, we get the best complexity bound of wide neighborhood interior-point algorithm for symmetric cone programming.
引用本文（GB/T 7714）
Changhe Liu, Youlin Shang, HongWei LIU. 对称锥规划的邻域跟踪算法[J]. Scientia Sinica Mathematica, 2013.
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