Aug 20, 2000 #3 M me2please Guest 给定一个锥 <img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$K' title="3 $亩" alt='3$K' align=absmiddle> <img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$y \in K = \{Ax|x\geq 0\}' title="3 $ ý \在K = \(斧| x \固尔奇0 \)" alt='3$y \in K = \{Ax|x\geq 0\}' align=absmiddle>对偶集 <img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$K^{\ast}' title="3 $亩^(\阿斯特)" alt='3$K^{\ast}' align=absmiddle> 被定义为<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$x^{\ast} \in K^{\ast}=\{y^{T}x^{\ast}\geq 0' title="3 $χ^(\阿斯特)\在K ^(\阿斯特)= \(ý ^(Ť)χ^(\阿斯特)\固尔奇0" alt='3$x^{\ast} \in K^{\ast}=\{y^{T}x^{\ast}\geq 0' align=absmiddle> 所有 <img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$y \in K \}' title="3 $ ý在K \ \)" alt='3$y \in K \}' align=absmiddle>那么<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$y^{T}x^{\ast}=(Ax)^{T}x^{\ast}=x^{T}(A^{T}x^{\ast})\geq 0' title="3 $ ý)^(Ťχ^(\阿斯特)=(AX)的^(Ť)χ^(\阿斯特)=χ^(Ť)(阿^(Ť)χ^(\阿斯特))\固尔奇0" alt='3$y^{T}x^{\ast}=(Ax)^{T}x^{\ast}=x^{T}(A^{T}x^{\ast})\geq 0' align=absmiddle>自从 <img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$x \geq 0' title="3 $ x \固尔奇0" alt='3$x \geq 0' align=absmiddle> ,对偶集<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$K^{\ast}=\{A^{T}x^{\ast}\geq0\}' title="3 $亩^(\阿斯特)= \(甲)^(Ťχ^(\阿斯特)\ geq0 \)" alt='3$K^{\ast}=\{A^{T}x^{\ast}\geq0\}' align=absmiddle>这是一个多面体锥的半空间已通过原产地通过相应halfplanes有限数目(路口。)
给定一个锥 <img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$K' title="3 $亩" alt='3$K' align=absmiddle> <img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$y \in K = \{Ax|x\geq 0\}' title="3 $ ý \在K = \(斧| x \固尔奇0 \)" alt='3$y \in K = \{Ax|x\geq 0\}' align=absmiddle>对偶集 <img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$K^{\ast}' title="3 $亩^(\阿斯特)" alt='3$K^{\ast}' align=absmiddle> 被定义为<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$x^{\ast} \in K^{\ast}=\{y^{T}x^{\ast}\geq 0' title="3 $χ^(\阿斯特)\在K ^(\阿斯特)= \(ý ^(Ť)χ^(\阿斯特)\固尔奇0" alt='3$x^{\ast} \in K^{\ast}=\{y^{T}x^{\ast}\geq 0' align=absmiddle> 所有 <img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$y \in K \}' title="3 $ ý在K \ \)" alt='3$y \in K \}' align=absmiddle>那么<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$y^{T}x^{\ast}=(Ax)^{T}x^{\ast}=x^{T}(A^{T}x^{\ast})\geq 0' title="3 $ ý)^(Ťχ^(\阿斯特)=(AX)的^(Ť)χ^(\阿斯特)=χ^(Ť)(阿^(Ť)χ^(\阿斯特))\固尔奇0" alt='3$y^{T}x^{\ast}=(Ax)^{T}x^{\ast}=x^{T}(A^{T}x^{\ast})\geq 0' align=absmiddle>自从 <img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$x \geq 0' title="3 $ x \固尔奇0" alt='3$x \geq 0' align=absmiddle> ,对偶集<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$K^{\ast}=\{A^{T}x^{\ast}\geq0\}' title="3 $亩^(\阿斯特)= \(甲)^(Ťχ^(\阿斯特)\ geq0 \)" alt='3$K^{\ast}=\{A^{T}x^{\ast}\geq0\}' align=absmiddle>这是一个多面体锥的半空间已通过原产地通过相应halfplanes有限数目(路口。)