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clarification

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Steven G. Johnson 2023-04-09 16:47:21 -04:00
parent 3f10441047
commit b48f19aadb
1 changed files with 16 additions and 8 deletions
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psets/pset5.ipynb
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@ -2,7 +2,7 @@
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{ {
"cell_type": "markdown", "cell_type": "markdown",
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"# 18.065 Problem Set 5\n", "# 18.065 Problem Set 5\n",
@ -12,7 +12,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
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"## Problem 1 (5+6 points)\n", "## Problem 1 (5+6 points)\n",
@ -32,7 +32,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
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"source": [ "source": [
"## Problem 2 (5+6+6 points)\n", "## Problem 2 (5+6+6 points)\n",
@ -67,7 +67,7 @@
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{ {
@ -97,7 +97,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 52, "execution_count": 52,
"id": "cb117722", "id": "e5a615e1",
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{ {
@ -117,12 +117,12 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "ba18e276", "id": "7878762b",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Problem 3 (5+5+6 points)\n", "## Problem 3 (5+5+6 points)\n",
"\n", "\n",
"Solve the optimization problem from 2c above, with the same parameters, by implementing ADMM for the problem\n", "In this problem, you will use ADMM to solve the (primal) optimization problem from problem 2 above, for the parameters from problem 2c, using the equivalent formulation:\n",
"$$\n", "$$\n",
"\\min_{x \\in \\mathbb{R}^n} \\left( \\Vert b - Ax \\Vert_2^2 + \\begin{cases} 0 & \\Vert x \\Vert_2 \\le r \\\\ \\infty & \\mbox{otherwise} \\end{cases} \\right)\n", "\\min_{x \\in \\mathbb{R}^n} \\left( \\Vert b - Ax \\Vert_2^2 + \\begin{cases} 0 & \\Vert x \\Vert_2 \\le r \\\\ \\infty & \\mbox{otherwise} \\end{cases} \\right)\n",
"$$\n", "$$\n",
@ -138,8 +138,16 @@
"\n", "\n",
"**(b)** Give a closed-form solution for step 2.\n", "**(b)** Give a closed-form solution for step 2.\n",
"\n", "\n",
"**(c)** Implement this iteration in Julia to solve problem 2c, starting from $x = z = s = \\vec{0}$. Make a (semi-log) plot of the error $\\Vert x^{(k)} - x_* \\Vert_2$ versus $k$, where $x_*$ is your solution from 2c, for $\\rho = 1$ and $\\rho = 10$. (The error should converge to zero!)" "**(c)** Implement this iteration in Julia to solve this problem with the parameters from 2c above, starting from $x = z = s = \\vec{0}$. Make a (semi-log) plot of the error $\\Vert x^{(k)} - x_* \\Vert_2$ versus $k$, where $x_*$ is your solution from 2c, for $\\rho = 1$ and $\\rho = 10$. (The error should converge to zero!)"
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"source": []
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