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<p><?tk 2?>In this paper, we are interested in the study of finding robust efficient solutions in vector rational optimization problems with SOS-convex polynomials under data uncertainty. In order to solve such a class of vector rational optimization problems, we provide a mixed-type method consisting of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10479_2025_6938_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> </InlineEquation>-constraint method for vector optimization, the parameter-free approach for rational optimization, and the exact SDP-based relaxation method for SOS-convex polynomial programs. We also give a procedure (with a detailed computed example) to show how our method works.</p>

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Solving a class of robust vector rational optimization problems

  • 期刊论文

  • 发表日期：

    2025年11月13日

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  • Jian Huang,
  • Liguo Jiao,
  • Jae Hyoung Lee,
  • Chengmiao Yang,
  • Junping Yin

摘要

In this paper, we are interested in the study of finding robust efficient solutions in vector rational optimization problems with SOS-convex polynomials under data uncertainty. In order to solve such a class of vector rational optimization problems, we provide a mixed-type method consisting of the \(\varepsilon \) -constraint method for vector optimization, the parameter-free approach for rational optimization, and the exact SDP-based relaxation method for SOS-convex polynomial programs. We also give a procedure (with a detailed computed example) to show how our method works.