Interior-point methods for monotone linear complementarity problems based on the new kernel function with applications to control tabular adjustment problem

We present a feasible kernel-based interior point method (IPM) to solve the monotone linear complementarity problem (LCP) which is based on an eligible kernel function with a new logarithmic barrier term. This kernel function defines the new search direction and the neighborhood of the central path. We show the global convergence of the algorithm and derive the iteration bounds for short- and long-step versions of the algorithm. We applied the method to solve a continuous Control Tabular Adjustment (CTA) problem which is an important Statistical Disclosure Limitation (SDL) model for protection of tabular data. Numerical results on a test example show that this algorithm is a viable option to the existing methods for solving continuous CTA problems. We also apply the algorithm to the set of randomly generated monotone LCPs showing that the initial implementation performs well on these instances of LCPs. However, this limited numerical testing is done for illustration purposes; an extensive numerical study is necessary to draw more definite conclusions on the behavior of the algorithm.