We present a feasible full step interior-point algorithm to solve the $P_{\ast }(\kappa )$ horizontal linear complementarity problem defined on a Cartesian product of symmetric cones, which is not based on a usual barrier function. The full steps are scaled utilizing the Nesterov-Todd (NT) scaling point. Our approach generates the search directions leading to the full-NT steps by algebraically transforming the centring equation of the system which defines the central trajectory using the induced barrier of a so-called positive-asymptotic kernel function. We establish the global convergence as well as a local quadratic rate of convergence of our proposed method. Finally, we demonstrate that our algorithm bears a complexity bound matching the best available one for the algorithms of its kind.

我们提出了一种可行的全步内点算法来解决${磷}_{*}(\kappa )$在对称锥的笛卡尔积上定义的水平线性互补问题，它不是基于通常的障碍函数。使用 Nesterov-Todd (NT) 缩放点缩放完整的步骤。我们的方法通过使用所谓的正渐近核函数的诱导障碍对定义中心轨迹的系统的中心方程进行代数变换来生成通向全 NT 步骤的搜索方向。我们建立了我们提出的方法的全局收敛性和局部二次收敛率。最后，我们证明了我们的算法具有与同类算法中最佳可用算法相匹配的复杂性界限。