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

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 $\mathrm{T}\mathrm{L}\mathrm{C}\mathrm{P}$ is established. In addition, sufficient conditions for uniqueness and for feasibility implying solvability are derived.