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<p>The main propose of the present paper is to investigate the finiteness property of the solution set for the extended vertical tensor complementarity problem (EVTCP). To this end, two classes of structured tensor tuples, that is, vertical non-degenerate (VND) tensor tuples and strong vertical non-degenerate (SVND) tensor tuples , are introduced. Furthermore, the relationship and some properties about them are discussed. Based on the structured tensor tuples, the finiteness property of the solution set of EVTCP is investigated. The results obtained in this paper are extensions of those proposed by Palpandi and Sharma (J Optim Theory Appl 190:951–965, 2021) from the tensor complementarity problem (TCP) to EVTCP.</p>

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Extended vertical tensor complementarity problems with finite solution sets

  • 期刊论文

  • 发表日期：

    2025年2月28日

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  • Xue-liu Li,
  • Yi-rong Jiang,
  • Yuning Yang,
  • Guo-ji Tang

摘要

The main propose of the present paper is to investigate the finiteness property of the solution set for the extended vertical tensor complementarity problem (EVTCP). To this end, two classes of structured tensor tuples, that is, vertical non-degenerate (VND) tensor tuples and strong vertical non-degenerate (SVND) tensor tuples , are introduced. Furthermore, the relationship and some properties about them are discussed. Based on the structured tensor tuples, the finiteness property of the solution set of EVTCP is investigated. The results obtained in this paper are extensions of those proposed by Palpandi and Sharma (J Optim Theory Appl 190:951–965, 2021) from the tensor complementarity problem (TCP) to EVTCP.