@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: a skos:ConceptScheme .
psr:-W42D202L-K
  skos:prefLabel "inégalité"@fr, "inequality"@en ;
  a skos:Concept ;
  skos:narrower psr:-RXNJS1M1-N .

psr:-RXNJS1M1-N
  skos:exactMatch <https://en.wikipedia.org/wiki/Linear_matrix_inequality>, <https://fr.wikipedia.org/wiki/In%C3%A9galit%C3%A9_matricielle_lin%C3%A9aire> ;
  skos:broader psr:-XJ7K95G7-L, psr:-W42D202L-K ;
  dc:created "2023-08-11"^^xsd:date ;
  skos:prefLabel "inégalité matricielle linéaire"@fr, "linear matrix inequality"@en ;
  skos:definition """En optimisation convexe, une <b>inégalité matricielle linéaire (Linear matricial inequality ou LMI)</b> est une expression de la forme
<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 LMI(y):=A_{0}+y_{1}A_{1}+y_{2}A_{2}+\\\\cdots +y_{m}A_{m}\\\\geq 0\\\\,}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>L</mi>
<br/>        <mi>M</mi>
<br/>        <mi>I</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>y</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>:=</mo>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>+</mo>
<br/>        <msub>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>+</mo>
<br/>        <msub>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>+</mo>
<br/>        <mo>⋯<!-- ⋯ --></mo>
<br/>        <mo>+</mo>
<br/>        <msub>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>m</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>m</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>≥<!-- ≥ --></mo>
<br/>        <mn>0</mn>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle LMI(y):=A_{0}+y_{1}A_{1}+y_{2}A_{2}+\\\\cdots +y_{m}A_{m}\\\\geq 0\\\\,}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb2c9a9273e5c47f67d29308b44da90c57797830" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:49.651ex; height:2.843ex;" alt="{\\\\displaystyle LMI(y):=A_{0}+y_{1}A_{1}+y_{2}A_{2}+\\\\cdots +y_{m}A_{m}\\\\geq 0\\\\,}"></span></dd></dl>
<br/>où
<br/>
<br/><ul><li><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 y=[y_{i}\\\\,,~i\\\\!=\\\\!1\\\\dots m]}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>y</mi>
<br/>        <mo>=</mo>
<br/>        <mo stretchy="false">[</mo>
<br/>        <msub>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>i</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mo>,</mo>
<br/>        <mtext>&nbsp;</mtext>
<br/>        <mi>i</mi>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mo>=</mo>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mn>1</mn>
<br/>        <mo>…<!-- … --></mo>
<br/>        <mi>m</mi>
<br/>        <mo stretchy="false">]</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle y=[y_{i}\\\\,,~i\\\\!=\\\\!1\\\\dots m]}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/083109f7ac8cf6beef57a637460579441d4d1460" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:19.315ex; height:2.843ex;" alt="{\\\\displaystyle y=[y_{i}\\\\,,~i\\\\!=\\\\!1\\\\dots m]}"></span> est un vecteur réel,</li>
<br/><li><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 A_{0}\\\\,,A_{1}\\\\,,A_{2}\\\\,,\\\\dots \\\\,A_{m}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mo>,</mo>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mo>,</mo>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mo>,</mo>
<br/>        <mo>…<!-- … --></mo>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>m</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle A_{0}\\\\,,A_{1}\\\\,,A_{2}\\\\,,\\\\dots \\\\,A_{m}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6108fddbc2d133f59520780067c479f1411516d8" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:19.571ex; height:2.509ex;" alt="{\\\\displaystyle A_{0}\\\\,,A_{1}\\\\,,A_{2}\\\\,,\\\\dots \\\\,A_{m}}"></span> sont dans l'ensemble <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 S_{n}(\\\\mathbb {R} )}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>S</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="double-struck">R</mi>
<br/>        </mrow>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle S_{n}(\\\\mathbb {R} )}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f2f442337d31fb80064b70cfde40cbd594082c2" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:6.131ex; height:2.843ex;" alt="{\\\\displaystyle S_{n}(\\\\mathbb {R} )}"></span> des  matrices symétriques,</li>
<br/><li><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 B\\\\geq 0}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>B</mi>
<br/>        <mo>≥<!-- ≥ --></mo>
<br/>        <mn>0</mn>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle B\\\\geq 0}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db83a396bf5ff2d5b36198835c75b7b74b4f3ace" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:6.025ex; height:2.343ex;" alt="{\\\\displaystyle B\\\\geq 0}"></span> signifie que <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 B}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>B</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle B}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="B"></span> est une matrice semi-définie positive appartenant au sous-ensemble <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 S_{n}^{+}(\\\\mathbb {R} )}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msubsup>
<br/>          <mi>S</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mo>+</mo>
<br/>          </mrow>
<br/>        </msubsup>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="double-struck">R</mi>
<br/>        </mrow>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle S_{n}^{+}(\\\\mathbb {R} )}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7047a22af13bb37efc4347d80711a3a4357b74a9" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:6.52ex; height:3.009ex;" alt="{\\\\displaystyle S_{n}^{+}(\\\\mathbb {R} )}"></span> de l'ensemble des matrices symétriques <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 S_{n}(\\\\mathbb {R} )}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>S</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="double-struck">R</mi>
<br/>        </mrow>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle S_{n}(\\\\mathbb {R} )}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f2f442337d31fb80064b70cfde40cbd594082c2" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:6.131ex; height:2.843ex;" alt="{\\\\displaystyle S_{n}(\\\\mathbb {R} )}"></span>.</li></ul>
<br/>Cette inégalité matricielle linéaire caractérise un ensemble convexe selon <i>y</i>. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/In%C3%A9galit%C3%A9_matricielle_lin%C3%A9aire">https://fr.wikipedia.org/wiki/In%C3%A9galit%C3%A9_matricielle_lin%C3%A9aire</a>)"""@fr, """n convex optimization, a <b>linear matrix inequality</b> (<b>LMI</b>) is an expression of the form
<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 \\\\operatorname {LMI} (y):=A_{0}+y_{1}A_{1}+y_{2}A_{2}+\\\\cdots +y_{m}A_{m}\\\\succeq 0\\\\,}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>LMI</mi>
<br/>        <mo>⁡<!-- ⁡ --></mo>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>y</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>:=</mo>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>+</mo>
<br/>        <msub>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>+</mo>
<br/>        <msub>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>+</mo>
<br/>        <mo>⋯<!-- ⋯ --></mo>
<br/>        <mo>+</mo>
<br/>        <msub>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>m</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>m</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>⪰<!-- ⪰ --></mo>
<br/>        <mn>0</mn>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\operatorname {LMI} (y):=A_{0}+y_{1}A_{1}+y_{2}A_{2}+\\\\cdots +y_{m}A_{m}\\\\succeq 0\\\\,}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9146e5a3c0820b3321a9624832c9724496582f15" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:48.878ex; height:2.843ex;" alt="{\\\\displaystyle \\\\operatorname {LMI} (y):=A_{0}+y_{1}A_{1}+y_{2}A_{2}+\\\\cdots +y_{m}A_{m}\\\\succeq 0\\\\,}"></span></dd></dl>
<br/>where
<br/>
<br/><ul><li><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 y=[y_{i}\\\\,,~i\\\\!=\\\\!1,\\\\dots ,m]}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>y</mi>
<br/>        <mo>=</mo>
<br/>        <mo stretchy="false">[</mo>
<br/>        <msub>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>i</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mo>,</mo>
<br/>        <mtext>&nbsp;</mtext>
<br/>        <mi>i</mi>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mo>=</mo>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mn>1</mn>
<br/>        <mo>,</mo>
<br/>        <mo>…<!-- … --></mo>
<br/>        <mo>,</mo>
<br/>        <mi>m</mi>
<br/>        <mo stretchy="false">]</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle y=[y_{i}\\\\,,~i\\\\!=\\\\!1,\\\\dots ,m]}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89265d1d358a5bb9e6ecd14fd6636c804b30b94f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:20.996ex; height:2.843ex;" alt="y=[y_i\\\\,,~i\\\\!=\\\\!1,\\\\dots, m]"></span> is a real vector,</li>
<br/><li><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 A_{0},A_{1},A_{2},\\\\dots ,A_{m}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>,</mo>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>,</mo>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>,</mo>
<br/>        <mo>…<!-- … --></mo>
<br/>        <mo>,</mo>
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>m</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle A_{0},A_{1},A_{2},\\\\dots ,A_{m}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/505a2e5e84a1b5608bc4ab9c66639d73149d0934" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:19.056ex; height:2.509ex;" alt="A_0, A_1, A_2,\\\\dots,A_m"></span> are <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 n\\	imes n}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>n</mi>
<br/>        <mo>×<!-- × --></mo>
<br/>        <mi>n</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle n\\	imes n}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59d2b4cb72e304526cf5b5887147729ea259da78" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:5.63ex; height:1.676ex;" alt="n\\	imes n"></span> symmetric matrices <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 \\\\mathbb {S} ^{n}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">S</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {S} ^{n}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41c00c9d3635f5230e6ac11902a50f2323794ed6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.511ex; height:2.343ex;" alt="\\\\mathbb{S}^n"></span>,</li>
<br/><li><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 B\\\\succeq 0}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>B</mi>
<br/>        <mo>⪰<!-- ⪰ --></mo>
<br/>        <mn>0</mn>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle B\\\\succeq 0}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85560c0b200be0e93695e60cca637547156bb726" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:6.025ex; height:2.343ex;" alt="{\\\\displaystyle B\\\\succeq 0}"></span> is a generalized inequality meaning <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 B}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>B</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle B}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="B"></span> is a positive semidefinite matrix belonging to the positive semidefinite cone <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 \\\\mathbb {S} _{+}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">S</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mo>+</mo>
<br/>          </mrow>
<br/>        </msub>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {S} _{+}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f67309d1e894a7be81d045bd7ff08d3d3c35ee1d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.803ex; height:2.509ex;" alt="\\\\mathbb{S}_+"></span> in the subspace of symmetric matrices <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 \\\\mathbb {S} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="double-struck">S</mi>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {S} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f9d5874c5d7f68eba1cec9da9ccbe53903303bb" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.293ex; height:2.176ex;" alt="\\\\mathbb {S} "></span>.</li></ul>
<br/>This linear matrix inequality specifies a convex constraint on&nbsp;<i>y</i>. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Linear_matrix_inequality">https://en.wikipedia.org/wiki/Linear_matrix_inequality</a>)"""@en ;
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