LAUSR

Kernel functions play an important role in the design and complexity analysis of interior point algorithms for solving convex optimization problems. They determine both search directions and the proximity measure between the iterate and the central path. In this paper, we introduce a primal-dual interior point algorithm for solving $$P_*(\kappa ) $$-horizontal linear complementarity problems based on a new kernel function that has a trigonometric function in its barrier term. By using some simple analysis tools, we present some properties of the new kernel function. Our analysis shows that the algorithm meets the best known complexity bound i.e., $$O\left( (1+2\kappa )\sqrt{n}\log n\log \frac{n}{\varepsilon }\right) $$ for large-update methods. Finally, we present some numerical results illustrating the performance of the algorithm.