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Tensor quadratic eigenvalue complementarity problem. (English) Zbl 07379566

Summary: In this paper, we introduce a class of tensor quadratic eigenvalue complementarity problems, which is an interesting generalization of matrix quadratic eigenvalue complementarity problems on higher order tensors. We give a sufficient condition to guarantee the existence of solutions, and propose a semismooth Newton-type method to solve the tensor quadratic eigenvalue complementarity problem. Finally, some numerical results are reported to show the efficiency of the proposed method.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A69 Multilinear algebra, tensor calculus
15A18 Eigenvalues, singular values, and eigenvectors
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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