Interior-point methods for monotone linear complementarity problems based on the new kernel function with...

Area of Science:

• Optimization Methods
• Computational Mathematics
• Data Privacy

Background:

• Monotone linear complementarity problems (LCPs) are fundamental in various fields.
• Existing methods for solving LCPs and related problems like Control Tabular Adjustment (CTA) have limitations.
• Statistical Disclosure Limitation (SDL) models are crucial for protecting sensitive tabular data.

Purpose of the Study:

• To introduce a novel kernel-based interior point method (IPM) for solving monotone LCPs.
• To develop a new logarithmic barrier term and kernel function for IPMs.
• To assess the method's applicability to continuous CTA problems within SDL.

Main Methods:

• A feasible kernel-based interior point method (IPM) using a novel logarithmic barrier kernel function.
• Derivation of global convergence and iteration bounds for short- and long-step algorithms.
• Application to continuous Control Tabular Adjustment (CTA) problems and randomly generated monotone LCPs.

Main Results:

• The proposed IPM demonstrates global convergence.
• Iteration bounds were derived for both short- and long-step algorithms.
• Numerical results indicate the method is a viable option for continuous CTA problems and performs well on random LCP instances.

Conclusions:

• The developed kernel-based IPM is a promising approach for solving monotone LCPs.
• The method shows potential for application in Statistical Disclosure Limitation (SDL) through continuous CTA problems.
• Further extensive numerical studies are recommended to fully ascertain the algorithm's performance characteristics.