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<p>In this article, we introduce column adequate tensor in the context of tensor complementarity problem and consider some important properties. The tensor complementarity problem is a class of nonlinear complementarity problem with the involved function being defined by a tensor. We establish the inheritance property and invariance property of column adequate tensors. We study TCP<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((q,\mathcal {\varvec{A}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>q</mi> <mo>,</mo> <mrow> <mi mathvariant="bold-script">A</mi> </mrow> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> in the frame of LCP<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\((\bar{q},\bar{A})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mover accent="true"> <mrow> <mi>q</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mo>,</mo> <mover accent="true"> <mrow> <mi>A</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. We show that TCP<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\((q,\mathcal {\varvec{A}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>q</mi> <mo>,</mo> <mrow> <mi mathvariant="bold-script">A</mi> </mrow> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> has <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-unique solution under some assumptions.</p>

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On some properties of \( {\omega }\)-uniqueness in tensor complementarity problem

  • 期刊论文

  • 发表日期：

    2025年8月18日

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  • A. Dutta,
  • R. Deb,
  • A. K. Das

摘要

In this article, we introduce column adequate tensor in the context of tensor complementarity problem and consider some important properties. The tensor complementarity problem is a class of nonlinear complementarity problem with the involved function being defined by a tensor. We establish the inheritance property and invariance property of column adequate tensors. We study TCP \((q,\mathcal {\varvec{A}})\) ( q , A ) in the frame of LCP \((\bar{q},\bar{A})\) ( q ¯ , A ¯ ) . We show that TCP \((q,\mathcal {\varvec{A}})\) ( q , A ) has \(\omega \) ω -unique solution under some assumptions.