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<p>We propose in this paper a tighter underestimator for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2024_1235_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-nonconvex bivariate functions. We show that it is tighter than the classical <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2024_1235_Article_IEq2.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha -\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>BB underestimator. A branch and bound algorithm with this tighter underestimator is developed to solve bivariate global optimzation problems. The triangulation is used as an exhaustive subdivision, and a convex/concave test is added to accelerate the convergence of our branch and bound algorithm.</p>

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Tighter underestimator for bivariate global optimization

  • 期刊论文

  • 发表日期：

    2025年1月13日

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  • Mohand Ouanes

摘要

We propose in this paper a tighter underestimator for \(C^{2}\) C 2 -nonconvex bivariate functions. We show that it is tighter than the classical \(\alpha -\) α - BB underestimator. A branch and bound algorithm with this tighter underestimator is developed to solve bivariate global optimzation problems. The triangulation is used as an exhaustive subdivision, and a convex/concave test is added to accelerate the convergence of our branch and bound algorithm.