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<p>In a normed space <i>Y</i> with an order relation induced by a general set, we establish set relations, which are extensions of Kuroiwa’s, and some useful properties are provided. We introduce two generalized set scalarizations functions of type <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="186_2025_911_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sup \)</EquationSource> </InlineEquation>-<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="186_2025_911_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\inf \)</EquationSource> </InlineEquation>, which are extensions of the oriented distance of Hiriart-Urruty, and several essential properties are derived for them. We present various concepts of minimal solutions in a set optimization problem which extend and unify others that exist in the literature and, by using the above set scalarization, minimal solutions and weak minimal solutions for such problems are characterized.</p>

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Set scalarizations based on the oriented distance with respect to an arbitrary set and an application in set optimization

  • 期刊论文

  • 发表日期：

    2025年10月22日

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  • B. Jiménez,
  • V. Novo,
  • A. Vílchez

摘要

In a normed space Y with an order relation induced by a general set, we establish set relations, which are extensions of Kuroiwa’s, and some useful properties are provided. We introduce two generalized set scalarizations functions of type \(\sup \) - \(\inf \) , which are extensions of the oriented distance of Hiriart-Urruty, and several essential properties are derived for them. We present various concepts of minimal solutions in a set optimization problem which extend and unify others that exist in the literature and, by using the above set scalarization, minimal solutions and weak minimal solutions for such problems are characterized.