Interior-point methods for monotone linear complementarity problems based on the new kernel function with applications to Control Tabular Adjustment problem

  • Lesaja Goran Georgia Southern University, USA
  • Anna Oganian National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, MD, USA
  • Tifani Williams Mathematical Sciences, Georgia Southern University, Statesboro, Georgia, USA
  • Ionut Iacob Mathematical Sciences, Georgia Southern University, Statesboro, Georgia, USA
  • Mehtab Iqbal Clemson University, Clemson, South Carolina, USA
DOI: https://doi.org/10.19139/soic-2310-5070-2322
Keywords: linear complementarity problem, small-step and large-step interior-point methods, iteration bounds, polynomial complexity, control tabular adjustment problem

Abstract

We present a feasible kernel-based interior point method (IPM) to solve a monotone linear complementarity problem (LCP) which is based on an eligible kernel function with new logarithmic barrier term. The new kernel function defines 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 very limited numerical testing is done for illustration purposes only; an extensive numerical study is necessary to draw more definite conclusions on the behavior of the algorithm.

References

Listed in the Letter to the Editor (CoverLetter)
Published
2025-01-19
How to Cite
Goran, L., Oganian, A., Williams, T., Iacob, I., & Iqbal, M. (2025). Interior-point methods for monotone linear complementarity problems based on the new kernel function with applications to Control Tabular Adjustment problem. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2322
Issue
Online First
Section
Research Articles
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