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mhjensen
2020-11-27 14:30:19 +01:00
parent 9453f9ea93
commit d6e6109e22
8 changed files with 28 additions and 18 deletions
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doc/pub/week48/html/._week48-bs008.html
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@@ -270,7 +270,7 @@ We can rewrite this (see the solutions below) in terms of a convex optimization
$$
\begin{align*}
&\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber
&\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \hspace{0.2cm} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
&\mathrm{s.t} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \hspace{0.2cm} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
\end{align*}
$$
doc/pub/week48/html/._week48-bs013.html
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@@ -274,12 +274,14 @@ $$
\end{align*}
$$
Note: we use <b>s.t.</b> for subject to.
<b>Note</b>: we use <b>s.t.</b> for subject to.
<p>
Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem
$$
\begin{align*}
&\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}x^2+5x+3y \\ \nonumber
&\mathrm{subject to} \\ \nonumber
&\mathrm{s.t.} \\ \nonumber
&x, y \geq 0 \\ \nonumber
&x+3y \geq 15 \\ \nonumber
&2x+5y \leq 100 \\ \nonumber
doc/pub/week48/html/week48-reveal.html
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@@ -394,7 +394,7 @@ We can rewrite this (see the solutions below) in terms of a convex optimization
$$
\begin{align*}
&\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber
&\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \hspace{0.2cm} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
&\mathrm{s.t} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \hspace{0.2cm} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
\end{align*}
$$
<p>&nbsp;<br>
@@ -710,13 +710,15 @@ $$
$$
<p>&nbsp;<br>
Note: we use <b>s.t.</b> for subject to.
<b>Note</b>: we use <b>s.t.</b> for subject to.
<p>
Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem
<p>&nbsp;<br>
$$
\begin{align*}
&\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}x^2+5x+3y \\ \nonumber
&\mathrm{subject to} \\ \nonumber
&\mathrm{s.t.} \\ \nonumber
&x, y \geq 0 \\ \nonumber
&x+3y \geq 15 \\ \nonumber
&2x+5y \leq 100 \\ \nonumber
doc/pub/week48/html/week48-solarized.html
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@@ -429,7 +429,7 @@ We can rewrite this (see the solutions below) in terms of a convex optimization
$$
\begin{align*}
&\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber
&\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \hspace{0.2cm} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
&\mathrm{s.t} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \hspace{0.2cm} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
\end{align*}
$$
@@ -736,12 +736,14 @@ $$
\end{align*}
$$
Note: we use <b>s.t.</b> for subject to.
<b>Note</b>: we use <b>s.t.</b> for subject to.
<p>
Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem
$$
\begin{align*}
&\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}x^2+5x+3y \\ \nonumber
&\mathrm{subject to} \\ \nonumber
&\mathrm{s.t.} \\ \nonumber
&x, y \geq 0 \\ \nonumber
&x+3y \geq 15 \\ \nonumber
&2x+5y \leq 100 \\ \nonumber
doc/pub/week48/html/week48.html
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@@ -434,7 +434,7 @@ We can rewrite this (see the solutions below) in terms of a convex optimization
$$
\begin{align*}
&\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber
&\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \hspace{0.2cm} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
&\mathrm{s.t} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \hspace{0.2cm} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
\end{align*}
$$
@@ -741,12 +741,14 @@ $$
\end{align*}
$$
Note: we use <b>s.t.</b> for subject to.
<b>Note</b>: we use <b>s.t.</b> for subject to.
<p>
Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem
$$
\begin{align*}
&\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}x^2+5x+3y \\ \nonumber
&\mathrm{subject to} \\ \nonumber
&\mathrm{s.t.} \\ \nonumber
&x, y \geq 0 \\ \nonumber
&x+3y \geq 15 \\ \nonumber
&2x+5y \leq 100 \\ \nonumber
doc/pub/week48/ipynb/ipynb-week48-src.tar.gz
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doc/pub/week48/ipynb/week48.ipynb
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@@ -304,7 +304,7 @@
"$$\n",
"\\begin{align*}\n",
" &\\mathrm{min}_{\\lambda}\\hspace{0.2cm} \\frac{1}{2}\\boldsymbol{\\lambda}^T\\boldsymbol{P}\\boldsymbol{\\lambda}+\\boldsymbol{q}^T\\boldsymbol{\\lambda},\\\\ \\nonumber\n",
" &\\mathrm{subject\\hspace{0.1cm}to} \\hspace{0.2cm} \\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq \\boldsymbol{h} \\hspace{0.2cm} \\wedge \\boldsymbol{A}\\boldsymbol{\\lambda}=f.\n",
" &\\mathrm{s.t} \\hspace{0.2cm} \\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq \\boldsymbol{h} \\hspace{0.2cm} \\wedge \\boldsymbol{A}\\boldsymbol{\\lambda}=f.\n",
"\\end{align*}\n",
"$$"
]
@@ -650,7 +650,8 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Note: we use **s.t.** for subject to. \n",
"**Note**: we use **s.t.** for subject to. \n",
"\n",
"Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem"
]
},
@@ -661,7 +662,7 @@
"$$\n",
"\\begin{align*}\n",
" &\\mathrm{min}_{x}\\hspace{0.2cm} \\frac{1}{2}x^2+5x+3y \\\\ \\nonumber\n",
" &\\mathrm{subject to} \\\\ \\nonumber\n",
" &\\mathrm{s.t.} \\\\ \\nonumber\n",
" &x, y \\geq 0 \\\\ \\nonumber\n",
" &x+3y \\geq 15 \\\\ \\nonumber\n",
" &2x+5y \\leq 100 \\\\ \\nonumber\n",
doc/src/week48/week48.do.txt
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@@ -203,7 +203,7 @@ We can rewrite this (see the solutions below) in terms of a convex optimization
!bt
\begin{align*}
&\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\bm{\lambda}^T\bm{P}\bm{\lambda}+\bm{q}^T\bm{\lambda},\\ \nonumber
&\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \bm{G}\bm{\lambda} \preceq \bm{h} \hspace{0.2cm} \wedge \bm{A}\bm{\lambda}=f.
&\mathrm{s.t} \hspace{0.2cm} \bm{G}\bm{\lambda} \preceq \bm{h} \hspace{0.2cm} \wedge \bm{A}\bm{\lambda}=f.
\end{align*}
!et
Below we discuss how to solve these equations. Here we note that the matrix $\bm{P}$ has matrix elements $p_{ij}=y_iy_jK(\bm{x}_i,\bm{x}_j)$.
@@ -490,12 +490,13 @@ We remind ourselves about the general problem we want to solve
&\mathrm{s.t.} \hspace{0.2cm} \bm{G}\bm{x} \preceq \bm{h} \wedge \bm{A}\bm{x}=f.
\end{align*}
!et
Note: we use _s.t._ for subject to.
_Note_: we use _s.t._ for subject to.
Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem
!bt
\begin{align*}
&\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}x^2+5x+3y \\ \nonumber
&\mathrm{subject to} \\ \nonumber
&\mathrm{s.t.} \\ \nonumber
&x, y \geq 0 \\ \nonumber
&x+3y \geq 15 \\ \nonumber
&2x+5y \leq 100 \\ \nonumber