@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-FWTTZ9R7-X
  skos:prefLabel "fonction numérique à plusieurs variables réelles"@fr, "function of several real variables"@en ;
  a skos:Concept ;
  skos:narrower psr:-Q8H0F473-5 .

psr: a skos:ConceptScheme .
psr:-Q8H0F473-5
  skos:prefLabel "Himmelblau's function"@en, "fonction de Himmelblau"@fr ;
  skos:broader psr:-XJ7K95G7-L, psr:-FWTTZ9R7-X ;
  skos:definition """In mathematical optimization, <b>Himmelblau's function</b> is a multi-modal function, used to test the performance of optimization algorithms.  The function is defined by:
<br/>
<br/><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle f(x,y)=(x^{2}+y-11)^{2}+(x+y^{2}-7)^{2}.\\\\quad }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>f</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo>,</mo>
<br/>        <mi>y</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mo stretchy="false">(</mo>
<br/>        <msup>
<br/>          <mi>x</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>+</mo>
<br/>        <mi>y</mi>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mn>11</mn>
<br/>        <msup>
<br/>          <mo stretchy="false">)</mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>+</mo>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo>+</mo>
<br/>        <msup>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mn>7</mn>
<br/>        <msup>
<br/>          <mo stretchy="false">)</mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>.</mo>
<br/>        <mspace width="1em"></mspace>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle f(x,y)=(x^{2}+y-11)^{2}+(x+y^{2}-7)^{2}.\\\\quad }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c58cd364f39ccc8ae66ed6c693954bb44c829c62" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:43.175ex; height:3.176ex;" alt="f(x,y)=(x^{2}+y-11)^{2}+(x+y^{2}-7)^{2}.\\\\quad "> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Himmelblau%27s_function">https://en.wikipedia.org/wiki/Himmelblau%27s_function</a>)"""@en, """La <b>fonction de Himmelblau </b> est une fonction mathématique multimodale souvent utilisée pour évaluer la performance d'algorithmes d’optimisation. 
<br/>Elle est définie comme suit&nbsp;:
<br/><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle f(x,y)=(x^{2}+y-11)^{2}+(x+y^{2}-7)^{2}.\\\\quad }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>f</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo>,</mo>
<br/>        <mi>y</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mo stretchy="false">(</mo>
<br/>        <msup>
<br/>          <mi>x</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>+</mo>
<br/>        <mi>y</mi>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mn>11</mn>
<br/>        <msup>
<br/>          <mo stretchy="false">)</mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>+</mo>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo>+</mo>
<br/>        <msup>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mn>7</mn>
<br/>        <msup>
<br/>          <mo stretchy="false">)</mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>.</mo>
<br/>        <mspace width="1em"></mspace>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle f(x,y)=(x^{2}+y-11)^{2}+(x+y^{2}-7)^{2}.\\\\quad }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c58cd364f39ccc8ae66ed6c693954bb44c829c62" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:43.175ex; height:3.176ex;" alt="{\\\\displaystyle f(x,y)=(x^{2}+y-11)^{2}+(x+y^{2}-7)^{2}.\\\\quad }"> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_de_Himmelblau">https://fr.wikipedia.org/wiki/Fonction_de_Himmelblau</a>)"""@fr ;
  dc:created "2023-07-26"^^xsd:date ;
  a skos:Concept ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Fonction_de_Himmelblau>, <https://en.wikipedia.org/wiki/Himmelblau%27s_function> ;
  skos:inScheme psr: ;
  dc:modified "2023-07-26"^^xsd:date .

psr:-XJ7K95G7-L
  skos:prefLabel "optimization"@en, "optimisation"@fr ;
  a skos:Concept ;
  skos:narrower psr:-Q8H0F473-5 .