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"import numpy as np\n",
"import numpy.linalg as lin\n",
"import matplotlib.pylab as plt\n",
"import plotly.offline as py\n",
"import plotly.graph_objects as go\n",
"\n",
"%matplotlib inline\n",
"%config InlineBackend.figure_format = 'retina'\n",
"\n",
"np.set_printoptions(precision=3, linewidth=150, suppress=True)\n",
"plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])"
]
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"# Optimization problem\n",
"\n",
"An optimization problem looks like this:\n",
"\n",
"Given a function $J : ℝ^n \\rightarrow ℝ$, find the minimum of $J$ i.e. find ${\\bf u}$ such that\n",
"\n",
"$$J({\\bf u}) = \\inf_{{\\bf v} \\in ℝ^n} J({\\bf v})$$\n",
"\n",
"### Optimization problem with constraint\n",
"\n",
"It is possible to search for **u** not in $ℝ^n$ but in a part of $ℝ^n$, then it is a\n",
"constrained optimization problem.\n",
"\n",
"**Example** We are in 2D and we are looking for the minimum of $J(x,y)$ but with the constraint that $y > x$. This is equivalent to looking in the part of $ℝ^2$ that matches $y > x$.\n",
"\n",
"We will not look at optimization problems with constraints in this course but they are problems\n",
"important that you will see in your schooling.\n",
"\n",
"## The gradient method\n",
"\n",
"One way to solve a 2D optimization problem is to imagine it as terrain with relief. The\n",
"function $J(x,y)$ represents the altitude at any point $(x,y)$.\n",
"\n",
"To find the minimum of $J$ just start from a random point and go down in the direction that\n",
"goes down the most. A drop of water follows this path.\n",
"\n",
"This is the gradient method.\n",
"\n",
"To fully understand the method, it is necessary to fully understand the partial derivatives as well as the\n",
"notations which are summarized in this [memo on partial derivatives](https://www.lrde.epita.fr/~ricou/notations.pdf).\n",
"\n",
"The gradient algorithm is therefore:\n",
"\n",
"* take a random starting point ${\\bf p^0} = (x_0, y_0)$\n",
"* calculate the gradient of J at this point\n",
"\n",
"$$\n",
"\\nabla J(x_0, y_0) = \n",
"\\begin{bmatrix} \n",
"\\frac{\\partial J}{\\partial x} \\\\\n",
"\\frac{\\partial J}{\\partial y}\n",
"\\end{bmatrix} (x_0, y_0)\n",
"$$\n",
"* move in the opposite direction (the grandiant goes up): ${\\bf p}^{k+1} = {\\bf p}^k - \\mu \\, \\nabla J({\\bf p}^k)$\n",
"\n",
"and we repeat this last step until we arrive at a fixed point, i.e. that\n",
"$|| {\\bf p}^{k+1} - {\\bf p}^k|| < \\varepsilon$ with $\\varepsilon$ a very small value."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def J(x, y):\n",
" return x**2 + 0.5 * y**2 - 2 * x + 3"
]
},
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"text/plain": [
""
]
},
"metadata": {
"image/png": {
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},
"output_type": "display_data"
}
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"source": [
"plt.plot(x[:,0], x[:,1], 'x:')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
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\n",
"text/plain": [
""
]
},
"metadata": {
"image/png": {
"height": 246,
"width": 383
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# µ = 2\n",
"\n",
"x = minimum_J(start_value = (0,1), µ = 2)\n",
"plt.plot(x[:,0], x[:,1], 'x:')"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"marker": {
"size": 3
},
"type": "scatter3d",
"x": [
0,
4,
-8,
28,
-80,
244,
-728,
2188
],
"y": [
1,
-1,
1,
-1,
1,
-1,
1,
-1
],
"z": [
3.5,
11.5,
83.5,
731.5,
6563.5,
59051.5,
531443.5,
4782971.5
]
}
],
"layout": {
"template": {
"data": {
"bar": [
{
"error_x": {
"color": "#2a3f5f"
},
"error_y": {
"color": "#2a3f5f"
},
"marker": {
"line": {
"color": "#E5ECF6",
"width": 0.5
}
},
"type": "bar"
}
],
"barpolar": [
{
"marker": {
"line": {
"color": "#E5ECF6",
"width": 0.5
}
},
"type": "barpolar"
}
],
"carpet": [
{
"aaxis": {
"endlinecolor": "#2a3f5f",
"gridcolor": "white",
"linecolor": "white",
"minorgridcolor": "white",
"startlinecolor": "#2a3f5f"
},
"baxis": {
"endlinecolor": "#2a3f5f",
"gridcolor": "white",
"linecolor": "white",
"minorgridcolor": "white",
"startlinecolor": "#2a3f5f"
},
"type": "carpet"
}
],
"choropleth": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"type": "choropleth"
}
],
"contour": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0,
"#0d0887"
],
[
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],
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],
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],
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],
[
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],
[
0.6666666666666666,
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[
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],
[
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"#fdca26"
],
[
1,
"#f0f921"
]
],
"type": "contour"
}
],
"contourcarpet": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"type": "contourcarpet"
}
],
"heatmap": [
{
"colorbar": {
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"ticks": ""
},
"colorscale": [
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],
[
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]
],
"type": "heatmap"
}
],
"heatmapgl": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0,
"#0d0887"
],
[
0.1111111111111111,
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],
[
0.2222222222222222,
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[
0.3333333333333333,
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[
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[
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],
[
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],
[
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],
"type": "heatmapgl"
}
],
"histogram": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "histogram"
}
],
"histogram2d": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
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],
[
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],
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]
],
"type": "histogram2d"
}
],
"histogram2dcontour": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
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],
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"text/plain": [
""
]
},
"metadata": {
"image/png": {
"height": 246,
"width": 369
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# µ = 0.8\n",
"\n",
"x = minimum_J(start_value = (0,1), µ = 0.8)\n",
"plt.plot(x[:,0], x[:,1], 'x:')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
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\n",
"text/plain": [
""
]
},
"metadata": {
"image/png": {
"height": 246,
"width": 369
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# µ = 1\n",
"\n",
"x = minimum_J(start_value = (0,1), µ = 1)\n",
"plt.plot(x[:,0], x[:,1], 'x:')"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"marker": {
"size": 3
},
"type": "scatter3d",
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