Tensor Complementarity Problems with Finite Solution Sets

K. Palpandi () and Sonali Sharma ()
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K. Palpandi: Malaviya National Institute of Technology Jaipur
Sonali Sharma: Malaviya National Institute of Technology Jaipur

Journal of Optimization Theory and Applications, 2021, vol. 190, issue 3, No 11, 965 pages

Abstract: Abstract In this paper, we first extend the concept of non-degenerate matrices to tensors and we then study the finiteness properties of the solution set of non-degenerate tensor complementarity problems. When the involving tensor in the tensor complementarity problem is a positive linear combination of rank-one symmetric tensors, we show that the solution set of the tensor complementarity problem is convex if the underlying tensor is positive semidefinite, and the tensor complementarity problem has the globally uniqueness solvable property if the underlying tensor is positive definite. Finally, we prove that a symmetric P tensor with an additional condition has the globally uniqueness solvable property.

Keywords: Tensors; Non-degenerate tensors; Sum of rank-one tensors; Positive definite tensors; Complementarity problems; 15A18; 15B48; 90C33 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-021-01917-9

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