A new search direction of IPM for horizontal linear complementarity problems - Gong, Xiaoyu; Xi, Lei; Yuan, Bo (Frontiers in Energy Research, 2023)
In this paper, we present a new search direction for horizontal linear complementarity problem. A vector-valued function is applied on the system of xy=μe, and which defines the central path. Usually, the way to get the equivalent form of the central path is used the square root function. But in our paper, we substitute a new search function formed by the different identity map which obtain the equivalent shape of the central path used the square root function and we get the new search directions from the Newton’s Method. Given this frame work, we prove polynomial complexity for the Newton directions, we show that the algorithm’s complexity is O(√n log n/ε)，which is selfsame with the best given algorithms for horizontal linear complementarity problem.