We present a short-step interior-point algorithm (IPA) for sufficient linear complementarity problems (LCPs) based on a new search direction. An algebraic equivalent transformation (AET) is used on the centrality equation of the central path system and Newton’s method is applied on this modified system. This technique was offered by Zsolt Darvay for linear optimization in 2002. Darvay first used the square root function as AET and in 2012 Darvay et al. applied this technique with an other transformation formed by the difference of the identity map and the square root function. We apply the AET technique with the new function to transform the central path equation of the sufficient LCPs. This technique leads to new search directions for the problem. We introduce an IPA with full Newton steps and prove that the iteration bound of the algorithm coincides with the best known one for sufficient LCPs. We present some numerical results to illustrate performance of the proposed IPA on two significantly different sets of test problems and compare it, with related, quite similar variants of IPAs.

我们提出了一种基于新搜索方向的足够线性互补问题（LCP）的短步内点算法（IPA）。在中心路径系统的中心性方程式上使用了代数等效变换（AET），在此修改后的系统上应用了牛顿法。Zsolt Darvay在2002年为线性优化提供了这项技术。Darvay最早在2002年使用平方根函数作为AET，Darvay等人在2012年提出了此技术。将该技术与由身份图和平方根函数之差形成的其他变换一起应用。我们将AET技术与新功能一起应用，以转换足够LCP的中心路径方程。该技术导致了该问题的新搜索方向。我们介绍了具有完整牛顿步骤的IPA，并证明了该算法的迭代范围与已知的针对足够LCP的迭代范围一致。我们提供一些数值结果来说明所提出的IPA在两组明显不同的测试问题上的性能，并将其与IPA的相关，非常相似的变体进行比较。