On the R${}_0$-tensors and the solution map of tensor complementarity problems

Abstract

Our purpose is to investigate the local boundedness, the upper semicontinuity, and the stability of the solution map of tensor complementarity problems. To do this, we focus on the set of R${}_0$--tensors and show that this set plays an important role in the investigation. Furthermore, by using a technique in semi-algebraic geometry, we obtain some results on the finite-valuedness and the lower semicontinuity of the solution map.

20 pages

References in corpus (5)

• Properties of Solution set of Tensor Complementarity Problem
• Strictly semi-positive tensors and the boundedness of tensor complementarity problems
• Polynomial complementarity problems
• B tensors and tensor complementarity problems
• A mixed integer programming approach to the tensor complementarity problem

Cited by in corpus (1)

• Univariate representations of solutions to generic polynomial complementarity problems