In this paper, we present a new predictor-corrector interior-point algorithm based on a wide neighborhood for semidefinite optimization. The proposed algorithm is a Mizuno-Todd-Ye predictor-corrector type and uses the Nesterov-Todd (NT) search direction in predictor step and a commutative class of search directions involving Helmberg-Kojima-Monteiro and NT directions in corrector step. We show that the proposed algorithm at every both predictor and corrector steps reduces the duality gap. The method enjoys the iteration complexity of \({\mathcal {O}}(\sqrt{n\kappa _{\infty }}L)\), which matching to the currently best known iteration bound for wide neighborhood algorithms. Numerical results also confirm the algorithm is reliable and promising.

在本文中，我们提出了一种新的基于宽邻域的预测校正内点算法，用于半定优化。所提出的算法是 Mizuno-Todd-Ye 预测器-校正器类型，并在预测器步骤中使用 Nesterov-Todd (NT) 搜索方向，在校正器步骤中使用涉及 Helmberg-Kojima-Monteiro 和 NT 方向的交换类搜索方向。我们表明，所提出的算法在每个预测器和校正器步骤都减少了二元性差距。该方法具有\({\mathcal {O}}(\sqrt{n\kappa _{\infty }}L)\)的迭代复杂度，它与当前最知名的广邻域算法迭代边界相匹配。数值结果也证实了该算法是可靠和有前途的。