Kernel-Based and Learning-Based Interior-Point Method for Linear Complementarity Problems

This work introduces a theoretical framework of kernel-based and learning-based interior-point methods (IPMs) for $P_{*}(\kappa)$-linear complementarity problems (LCPs). We begin by presenting the traditional kernel-based IPM for LCP. Next, we integrate L2O option that uses Long Short-Term Memory (LSTM) neural networks to approximate linear system solutions at each iteration of the original algorithm. The proposed IPM-LSTM algorithmic framework is an alternative to previously developed approaches of inexact and iterative IPMs. The proposed methodology may also be computationally beneficial, which will be the topic of forthcoming research.