+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 $$ \begin{align*} @@ -313,15 +313,15 @@ The following code solves the equations for us import numpy from cvxopt import matrix from cvxopt import solvers -P = matrix(numpy.diag([1,0]), tc=’d’) -q = matrix(numpy.array([3,4]), tc=’d’) -G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’) -h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’) +P = matrix(numpy.diag([1,0]), tc='d') +q = matrix(numpy.array([3,4]), tc='d') +G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc='d') +h = matrix(numpy.array([0,0,-15,100,80]), tc='d') # Construct the QP, invoke solver sol = solvers.qp(P,q,G,h) # Extract optimal value and solution -sol[’x’] -sol[’primal objective’] +sol['x'] +sol['primal objective']
diff --git a/doc/pub/week48/html/._week48-bs015.html b/doc/pub/week48/html/._week48-bs015.html index 2f2a0ee84..dff4b8890 100644 --- a/doc/pub/week48/html/._week48-bs015.html +++ b/doc/pub/week48/html/._week48-bs015.html @@ -265,7 +265,7 @@ We have the general problem $$ \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} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f. + &\mathrm{s.t.} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f. \end{align*} $$ diff --git a/doc/pub/week48/html/week48-reveal.html b/doc/pub/week48/html/week48-reveal.html index 7bdb8c9c1..a8e9d41b4 100644 --- a/doc/pub/week48/html/week48-reveal.html +++ b/doc/pub/week48/html/week48-reveal.html @@ -697,12 +697,12 @@ We remind ourselves about the general problem we want to solve $$ \begin{align*} &\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}\boldsymbol{x}^T\boldsymbol{P}\boldsymbol{x}+\boldsymbol{q}^T\boldsymbol{x},\\ \nonumber - &\mathrm{subject\hspace{0.1cm} to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{x} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{x}=f. + &\mathrm{s.t.} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{x} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{x}=f. \end{align*} $$
-
+Note: we use s.t. for subject to. Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem
$$
@@ -756,15 +756,15 @@ The following code solves the equations for us
import numpy
from cvxopt import matrix
from cvxopt import solvers
-P = matrix(numpy.diag([1,0]), tc=’d’)
-q = matrix(numpy.array([3,4]), tc=’d’)
-G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)
-h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’)
+P = matrix(numpy.diag([1,0]), tc='d')
+q = matrix(numpy.array([3,4]), tc='d')
+G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc='d')
+h = matrix(numpy.array([0,0,-15,100,80]), tc='d')
# Construct the QP, invoke solver
sol = solvers.qp(P,q,G,h)
# Extract optimal value and solution
-sol[’x’]
-sol[’primal objective’]
+sol['x']
+sol['primal objective']
@@ -800,7 +800,7 @@ We have the general problem
$$
\begin{align*}
&\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber
- &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
+ &\mathrm{s.t.} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
\end{align*}
$$
diff --git a/doc/pub/week48/html/week48-solarized.html b/doc/pub/week48/html/week48-solarized.html
index 026699991..5cabd62ef 100644
--- a/doc/pub/week48/html/week48-solarized.html
+++ b/doc/pub/week48/html/week48-solarized.html
@@ -720,11 +720,11 @@ We remind ourselves about the general problem we want to solve
$$
\begin{align*}
&\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}\boldsymbol{x}^T\boldsymbol{P}\boldsymbol{x}+\boldsymbol{q}^T\boldsymbol{x},\\ \nonumber
- &\mathrm{subject\hspace{0.1cm} to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{x} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{x}=f.
+ &\mathrm{s.t.} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{x} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{x}=f.
\end{align*}
$$
-
+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 $$ \begin{align*} @@ -768,15 +768,15 @@ The following code solves the equations for us import numpy from cvxopt import matrix from cvxopt import solvers -P = matrix(numpy.diag([1,0]), tc=’d’) -q = matrix(numpy.array([3,4]), tc=’d’) -G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’) -h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’) +P = matrix(numpy.diag([1,0]), tc='d') +q = matrix(numpy.array([3,4]), tc='d') +G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc='d') +h = matrix(numpy.array([0,0,-15,100,80]), tc='d') # Construct the QP, invoke solver sol = solvers.qp(P,q,G,h) # Extract optimal value and solution -sol[’x’] -sol[’primal objective’] +sol['x'] +sol['primal objective']
@@ -808,7 +808,7 @@ We have the general problem
$$
\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} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
+ &\mathrm{s.t.} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
\end{align*}
$$
diff --git a/doc/pub/week48/html/week48.html b/doc/pub/week48/html/week48.html
index be0846702..62712fe3c 100644
--- a/doc/pub/week48/html/week48.html
+++ b/doc/pub/week48/html/week48.html
@@ -725,11 +725,11 @@ We remind ourselves about the general problem we want to solve
$$
\begin{align*}
&\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}\boldsymbol{x}^T\boldsymbol{P}\boldsymbol{x}+\boldsymbol{q}^T\boldsymbol{x},\\ \nonumber
- &\mathrm{subject\hspace{0.1cm} to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{x} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{x}=f.
+ &\mathrm{s.t.} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{x} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{x}=f.
\end{align*}
$$
-
+Note: we use s.t. for subject to. Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem $$ \begin{align*} @@ -773,15 +773,15 @@ The following code solves the equations for us import numpy from cvxopt import matrix from cvxopt import solvers -P = matrix(numpy.diag([1,0]), tc=’d’) -q = matrix(numpy.array([3,4]), tc=’d’) -G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’) -h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’) +P = matrix(numpy.diag([1,0]), tc='d') +q = matrix(numpy.array([3,4]), tc='d') +G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc='d') +h = matrix(numpy.array([0,0,-15,100,80]), tc='d') # Construct the QP, invoke solver sol = solvers.qp(P,q,G,h) # Extract optimal value and solution -sol[’x’] -sol[’primal objective’] +sol['x'] +sol['primal objective']
@@ -813,7 +813,7 @@ We have the general problem
$$
\begin{align*}
&\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber
- &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
+ &\mathrm{s.t.} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
\end{align*}
$$
diff --git a/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz b/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz
index f1c2daebe..4b9dbbba2 100644
Binary files a/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz and b/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz differ
diff --git a/doc/pub/week48/ipynb/week48.ipynb b/doc/pub/week48/ipynb/week48.ipynb
index 5dd1f2f42..b1656ffc5 100644
--- a/doc/pub/week48/ipynb/week48.ipynb
+++ b/doc/pub/week48/ipynb/week48.ipynb
@@ -634,7 +634,7 @@
"$$\n",
"\\begin{align*}\n",
" &\\mathrm{min}_{x}\\hspace{0.2cm} \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{P}\\boldsymbol{x}+\\boldsymbol{q}^T\\boldsymbol{x},\\\\ \\nonumber\n",
- " &\\mathrm{subject\\hspace{0.1cm} to} \\hspace{0.2cm} \\boldsymbol{G}\\boldsymbol{x} \\preceq \\boldsymbol{h} \\wedge \\boldsymbol{A}\\boldsymbol{x}=f.\n",
+ " &\\mathrm{s.t.} \\hspace{0.2cm} \\boldsymbol{G}\\boldsymbol{x} \\preceq \\boldsymbol{h} \\wedge \\boldsymbol{A}\\boldsymbol{x}=f.\n",
"\\end{align*}\n",
"$$"
]
@@ -643,6 +643,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
+ "Note: we use **s.t.** for subject to. \n",
"Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem"
]
},
@@ -747,15 +748,15 @@
"import numpy\n",
"from cvxopt import matrix\n",
"from cvxopt import solvers\n",
- "P = matrix(numpy.diag([1,0]), tc=’d’)\n",
- "q = matrix(numpy.array([3,4]), tc=’d’)\n",
- "G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)\n",
- "h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’)\n",
+ "P = matrix(numpy.diag([1,0]), tc='d')\n",
+ "q = matrix(numpy.array([3,4]), tc='d')\n",
+ "G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc='d')\n",
+ "h = matrix(numpy.array([0,0,-15,100,80]), tc='d')\n",
"# Construct the QP, invoke solver\n",
"sol = solvers.qp(P,q,G,h)\n",
"# Extract optimal value and solution\n",
- "sol[’x’] \n",
- "sol[’primal objective’]"
+ "sol['x'] \n",
+ "sol['primal objective']"
]
},
{
@@ -802,7 +803,7 @@
"$$\n",
"\\begin{align*}\n",
" &\\mathrm{min}_{\\lambda}\\hspace{0.2cm} \\frac{1}{2}\\boldsymbol{\\lambda}^T\\boldsymbol{P}\\boldsymbol{\\lambda}+\\boldsymbol{q}^T\\boldsymbol{\\lambda},\\\\ \\nonumber\n",
- " &\\mathrm{subject\\hspace{0.1cm}to} \\hspace{0.2cm} \\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq \\boldsymbol{h} \\wedge \\boldsymbol{A}\\boldsymbol{\\lambda}=f.\n",
+ " &\\mathrm{s.t.} \\hspace{0.2cm} \\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq \\boldsymbol{h} \\wedge \\boldsymbol{A}\\boldsymbol{\\lambda}=f.\n",
"\\end{align*}\n",
"$$"
]
diff --git a/doc/src/week48/week48.do.txt b/doc/src/week48/week48.do.txt
index 3f1006fe2..98166a542 100644
--- a/doc/src/week48/week48.do.txt
+++ b/doc/src/week48/week48.do.txt
@@ -480,10 +480,10 @@ We remind ourselves about the general problem we want to solve
!bt
\begin{align*}
&\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}\bm{x}^T\bm{P}\bm{x}+\bm{q}^T\bm{x},\\ \nonumber
- &\mathrm{subject\hspace{0.1cm} to} \hspace{0.2cm} \bm{G}\bm{x} \preceq \bm{h} \wedge \bm{A}\bm{x}=f.
+ &\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.
Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem
!bt
\begin{align*}
@@ -529,15 +529,15 @@ The following code solves the equations for us
import numpy
from cvxopt import matrix
from cvxopt import solvers
-P = matrix(numpy.diag([1,0]), tc=’d’)
-q = matrix(numpy.array([3,4]), tc=’d’)
-G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)
-h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’)
+P = matrix(numpy.diag([1,0]), tc='d')
+q = matrix(numpy.array([3,4]), tc='d')
+G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc='d')
+h = matrix(numpy.array([0,0,-15,100,80]), tc='d')
# Construct the QP, invoke solver
sol = solvers.qp(P,q,G,h)
# Extract optimal value and solution
-sol[’x’]
-sol[’primal objective’]
+sol['x']
+sol['primal objective']
!ec
!split
@@ -566,12 +566,13 @@ We have the general problem
!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} \wedge \bm{A}\bm{\lambda}=f.
+ &\mathrm{s.t.} \hspace{0.2cm} \bm{G}\bm{\lambda} \preceq \bm{h} \wedge \bm{A}\bm{\lambda}=f.
\end{align*}
!et
+
o With a given kernel we can thus define the matrix $\bm{P}$.
o The matrix $\bm{P}$ has matrix elements $p_{ij}=y_iy_jK(\bm{x}_i,\bm{x}_j)$. Given a kernel $K$ and the targets $y_i$ this matrix is easy to set up.
o The vector $\bm{q}$ is zero.