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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.05777 |
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Table of Contents:
- Although a unique solution is guaranteed in the Linear complementarity problem (LCP) when the matrix $\mathbf{M}$ is positive definite, practical applications often involve cases where $\mathbf{M}$ is only positive semi-definite, leading to multiple possible solutions. However, empirical observations suggest that uniqueness can still emerge under certain structural conditions on the matrix $\mathbf{M}$ and vector $\mathbf{q}$. Motivated by an unresolved problem in nonlinear modeling for beam contact in directional drilling, this paper systematically investigates conditions under which a unique solution exists for LCPs with certain positive semi-definite matrices $\mathbf{M}$. We provide a rigorous proof demonstrating the existence and uniqueness of the solution for this specific case and extend our findings to establish a generalized framework applicable to broader classes of LCPs. This framework enhances the understanding of LCP uniqueness conditions and provides theoretical guarantees for solving real-world problems where positive semi-definite matrices $\mathbf{M}$ arise.