<p>In this article, we consider a non-smooth multiobjective fractional semi-infinite optimization problems with equilibrium constraints. The concept of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2403_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(S \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>S</mi> </math></EquationSource> </InlineEquation>-stationary point is stated in terms of Clarke subdifferential for the non-smooth multiobjective fractional semi-infinite optimization problems with equilibrium constraints. Under the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2403_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(S \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>S</mi> </math></EquationSource> </InlineEquation>-stationary point and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2403_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(E \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>E</mi> </math></EquationSource> </InlineEquation>-convexity assumptions, we developed an <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2403_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(E \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>E</mi> </math></EquationSource> </InlineEquation>-sufficient optimality condition for the considered model. Additionally, we have formulated the <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2403_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(E \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>E</mi> </math></EquationSource> </InlineEquation>-Mond-Weir and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2403_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(E \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>E</mi> </math></EquationSource> </InlineEquation>-Schaible type dual models, and further, <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2403_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(E \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>E</mi> </math></EquationSource> </InlineEquation>-weak, <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2403_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(E \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>E</mi> </math></EquationSource> </InlineEquation>-strong, and <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2403_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(E \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>E</mi> </math></EquationSource> </InlineEquation>-converse duality results are established for the proposed dual models under <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2403_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(E \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>E</mi> </math></EquationSource> </InlineEquation>-convexity assumptions and using the idea of <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2403_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(S \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>S</mi> </math></EquationSource> </InlineEquation>-stationary point. Moreover, the theoretical results of the work are also validated by citing non-trivial example.</p>

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Optimality and duality relations for multiobjective fractional semi-infinite optimization problems with equilibrium constraints

  • Bishal Biswas,
  • S. K. Gupta

摘要

In this article, we consider a non-smooth multiobjective fractional semi-infinite optimization problems with equilibrium constraints. The concept of \(S \) S -stationary point is stated in terms of Clarke subdifferential for the non-smooth multiobjective fractional semi-infinite optimization problems with equilibrium constraints. Under the \(S \) S -stationary point and \(E \) E -convexity assumptions, we developed an \(E \) E -sufficient optimality condition for the considered model. Additionally, we have formulated the \(E \) E -Mond-Weir and \(E \) E -Schaible type dual models, and further, \(E \) E -weak, \(E \) E -strong, and \(E \) E -converse duality results are established for the proposed dual models under \(E \) E -convexity assumptions and using the idea of \(S \) S -stationary point. Moreover, the theoretical results of the work are also validated by citing non-trivial example.