Structure of the w-solution set of the tensor complementarity problem

• Published in: Optimization Vol. 74; no. 1; pp. 81 - 104
• Main Authors: Sharma, Sonali, Palpandi, K., Yadav, Punit Kumar
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 02.01.2025
• Subjects: column adequate tensors; column competent tensors; complementarity problems; positive semidefinite tensors; Tensors
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2023.2245406

Motivated by the study of column competent and column adequate matrices in the standard linear complementarity problems, we define column competent tensor, column adequate tensor and study the underlying properties of these tensors. We establish equivalent conditions for a column adequate tensor within the class of symmetric tensors and Z tensors. We then introduce the $ {\mathbf{w}} $ w -solution set for the tensor complementarity problem and examine the uniqueness and finiteness of the $ {\mathbf{w}} $ w -solution set. At last, we define column competent property and prove that under some additional condition, column competent property gives the finiteness of the $ \mathbf{w} $ w -solution set of the corresponding tensor complementarity problem.