On the Convexity of the Solution Set of Linear Complementarity Problem over Tensor Spaces

Sonali Sharma; V. Vetrivel; Jein-Shan Chen

On the Convexity of the Solution Set of Linear Complementarity Problem over Tensor Spaces

Optimization and Control 2026-04-03 v1

Authors: Sonali Sharma , V. Vetrivel , Jein-Shan Chen

Abstract

This paper investigates the convexity of the solution set of the linear complementarity problems over tensor spaces (TLCPs). We introduce the notion of a $T$ -column sufficient tensor and study its properties and relationships with several structured tensors. An equivalent condition for the convexity of the solution set of the $\mathrm{TLCP}$ is established. In addition, sufficient conditions for uniqueness and for feasibility implying solvability are derived.

Keywords

linear complementarity problem tensor spaces convexity T-column sufficient tensor solution set

Cite

@article{arxiv.2604.02231,
  title  = {On the Convexity of the Solution Set of Linear Complementarity Problem over Tensor Spaces},
  author = {Sonali Sharma and V. Vetrivel and Jein-Shan Chen},
  journal= {arXiv preprint arXiv:2604.02231},
  year   = {2026}
}

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17 pages, comments are welcome

On the Convexity of the Solution Set of Linear Complementarity Problem over Tensor Spaces

Abstract

Keywords

Cite

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