clarification
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"cells": [
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{
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"cell_type": "markdown",
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"id": "fd786915",
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"id": "701e5077",
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"metadata": {},
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"source": [
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"# 18.065 Problem Set 5\n",
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},
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{
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"cell_type": "markdown",
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"id": "ff18eab8",
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"id": "74f502b8",
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"metadata": {},
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"source": [
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"## Problem 1 (5+6 points)\n",
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},
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{
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"cell_type": "markdown",
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"id": "87b4dd84",
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"id": "3a49c4b1",
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"metadata": {},
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"source": [
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"## Problem 2 (5+6+6 points)\n",
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{
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"cell_type": "code",
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"execution_count": 38,
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"id": "e95087fb",
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"id": "1a89466c",
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"metadata": {},
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"outputs": [
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{
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{
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"cell_type": "code",
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"execution_count": 52,
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"id": "cb117722",
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"id": "e5a615e1",
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"metadata": {},
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"outputs": [
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{
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},
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{
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"cell_type": "markdown",
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"id": "ba18e276",
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"id": "7878762b",
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"metadata": {},
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"source": [
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"## Problem 3 (5+5+6 points)\n",
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"\n",
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"Solve the optimization problem from 2c above, with the same parameters, by implementing ADMM for the problem\n",
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"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",
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"$$\n",
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"\\min_{x \\in \\mathbb{R}^n} \\left( \\Vert b - Ax \\Vert_2^2 + \\begin{cases} 0 & \\Vert x \\Vert_2 \\le r \\\\ \\infty & \\mbox{otherwise} \\end{cases} \\right)\n",
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"$$\n",
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"\n",
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"**(b)** Give a closed-form solution for step 2.\n",
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"\n",
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"**(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!)"
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"**(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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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "cfb0991c",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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