{"paper":{"title":"Properties of Tensor Complementarity Problem and Some Classes of Structured Tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Liqun Qi, Yisheng Song","submitted_at":"2014-11-29T14:47:43Z","abstract_excerpt":"This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor $\\mathcal{A}$ such that the tensor complementarity problem $(\\q, \\mathcal{A})$:\n  $$\\mbox{ finding } \\x \\in \\mathbb{R}^n\\mbox{ such that }\\x \\geq \\0, \\q + \\mathcal{A}\\x^{m-1} \\geq \\0, \\mbox{ and }\\x^\\top (\\q + \\mathcal{A}\\x^{m-1}) = 0, $$ has a solution for each vector $\\q \\in \\mathbb{R}^n$. Several subclasses of Q-tensors are given: P-tensors, R-tensors, strictly semi-positive tensors and semi-positive R$_0$-tensors. We prove that a nonnegative tensor is a Q-tensor if and only if all of its principal diagonal e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0113","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}