diff --git a/psets/pset5.ipynb b/psets/pset5.ipynb index 029142f..9150839 100644 --- a/psets/pset5.ipynb +++ b/psets/pset5.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "fd786915", + "id": "701e5077", "metadata": {}, "source": [ "# 18.065 Problem Set 5\n", @@ -12,7 +12,7 @@ }, { "cell_type": "markdown", - "id": "ff18eab8", + "id": "74f502b8", "metadata": {}, "source": [ "## Problem 1 (5+6 points)\n", @@ -32,7 +32,7 @@ }, { "cell_type": "markdown", - "id": "87b4dd84", + "id": "3a49c4b1", "metadata": {}, "source": [ "## Problem 2 (5+6+6 points)\n", @@ -67,7 +67,7 @@ { "cell_type": "code", "execution_count": 38, - "id": "e95087fb", + "id": "1a89466c", "metadata": {}, "outputs": [ { @@ -97,7 +97,7 @@ { "cell_type": "code", "execution_count": 52, - "id": "cb117722", + "id": "e5a615e1", "metadata": {}, "outputs": [ { @@ -117,12 +117,12 @@ }, { "cell_type": "markdown", - "id": "ba18e276", + "id": "7878762b", "metadata": {}, "source": [ "## Problem 3 (5+5+6 points)\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", "$$\n", "\\min_{x \\in \\mathbb{R}^n} \\left( \\Vert b - Ax \\Vert_2^2 + \\begin{cases} 0 & \\Vert x \\Vert_2 \\le r \\\\ \\infty & \\mbox{otherwise} \\end{cases} \\right)\n", "$$\n", @@ -138,8 +138,16 @@ "\n", "**(b)** Give a closed-form solution for step 2.\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!)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cfb0991c", + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": {