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

TL;DR

This paper explores the convexity of solution sets in tensor-based linear complementarity problems, introducing new tensor properties and conditions for convexity, uniqueness, and solvability.

Contribution

It introduces the concept of T-column sufficient tensors and establishes conditions linking tensor properties to solution set convexity.

Findings

Equivalent condition for convexity of TLCP solution set

Sufficient conditions for solution uniqueness

Conditions linking feasibility to solvability

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.