Properties of Solution Set of Tensor Complementarity Problem

Yisheng Song () and Gaohang Yu ()
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Yisheng Song: Henan Normal University
Gaohang Yu: Gannan Normal University

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 1, No 6, 85-96

Abstract: Abstract In this paper, a new subclass of tensors is introduced and it is proved that this class of new tensors can be defined by the feasible region of the corresponding tensor complementarity problem. Furthermore, the boundedness of solution set of the tensor complementarity problem is equivalent to the uniqueness of solution for such a problem with zero vector. For the tensor complementarity problem with a strictly semi-positive tensor, we proved the global upper bounds of its solution set. In particular, such upper bounds are closely associated with the smallest Pareto eigenvalue of such a tensor.

Keywords: Tensor complementarity; Strictly semi-positive tensor; Strictly copositive; Feasible vector; 47H15; 47H12; 34B10; 47A52; 47J10; 47H09; 15A48; 47H07 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (29)

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DOI: 10.1007/s10957-016-0907-0

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