From 87ae74f3b155ee2d65e9495f1faf197bde2307e0 Mon Sep 17 00:00:00 2001
From: Yang Shen <143472565+boki2924@users.noreply.github.com>
Date: Thu, 31 Aug 2023 01:24:33 +0800
Subject: [PATCH 1/2] Update README.md
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README.md | 2 +-
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# :wave: The Basics of GitHub
-
+**test test test !!!**
## 🤓 Course overview and learning outcomes
The goal of this course is to give you a brief introduction to GitHub. We’ll also provide you with materials for further learning and a few ideas to get you started on our platform. 🚀
From 9ca8067cabf173f4e32c7adc33ee4644adc7d21f Mon Sep 17 00:00:00 2001
From: Yang Shen <143472565+boki2924@users.noreply.github.com>
Date: Fri, 28 Feb 2025 20:09:58 -0600
Subject: [PATCH 2/2] =?UTF-8?q?=E4=BD=BF=E7=94=A8=20Colab=20=E5=88=9B?=
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HW8_CVXPY.ipynb | 512 ++++++++++++++++++++++++++++++++++++++++++++++++
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diff --git a/HW8_CVXPY.ipynb b/HW8_CVXPY.ipynb
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "view-in-github",
+ "colab_type": "text"
+ },
+ "source": [
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "G4o4xuDWGwrf"
+ },
+ "source": [
+ "# IMPORTANT:\n",
+ "Before you start coding, you must save a copy of this notebook to your own Google Drive. See `File > Save a copy in Drive`.\n",
+ "\n",
+ "If you forget to do this, your changes will be lost at the end of the session. If changes are being saved, you should see `All Changes Saved` to the right of the `Help` menu.\n",
+ "\n",
+ "You are free to download the .ipynb file and edit it using some other tool if you like. You do not need to use Google Colab if you are more familiar with another Jupyter environment.\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# Quick Introduction to CVXPY"
+ ],
+ "metadata": {
+ "id": "WYbhCplHb6Tf"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "7agH_0WuGwrh"
+ },
+ "source": [
+ "[CVXPY](http://www.cvxpy.org/en/latest/index.html) is a Python-embedded modeling language for convex optimization problems. It allows you to express your problem in a natural way that follows the math, rather than in the restrictive standard form required by solvers.\n",
+ "\n",
+ "In this Jupyter notebook, we will see some examples on how to solve optimization problems using cvxpy."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "lUyD7gRDGwrh"
+ },
+ "source": [
+ "## A Linear Program\n",
+ "\n",
+ "Let's start with a simple example of a Linear Program, i.e., an optimization problem with a linear objective and linear inequality constraints.\n",
+ "\n",
+ "$$\n",
+ "\\begin{align}\n",
+ "\\max \\; & 140x + 235y\\\\\n",
+ "\\textrm{s.t.}\\; & x + y \\leq 180,\\\\\n",
+ " & x + 2y \\leq 240,\\\\\n",
+ " & 3x + y \\leq 300\\\\\n",
+ " & x \\geq 0, y \\geq 0.\n",
+ "\\end{align}\n",
+ "$$\n",
+ "\n",
+ "Here is how you code this up and solve it using CVXPY."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "vEGW1SDKGwri"
+ },
+ "outputs": [],
+ "source": [
+ "import cvxpy as cp\n",
+ "import numpy\n",
+ "\n",
+ "# Create two scalar optimization variables\n",
+ "x = cp.Variable()\n",
+ "y = cp.Variable()\n",
+ "\n",
+ "# Create constraints\n",
+ "constraints = [x >= 0,\n",
+ " y >= 0,\n",
+ " x + y <= 180,\n",
+ " x + 2*y <= 240,\n",
+ " 3 * x + y <= 300]\n",
+ "#constraints.append(x**2+2*y**2 >= 1)\n",
+ "\n",
+ "# Form objective\n",
+ "obj = cp.Maximize(140*x +235*y)\n",
+ "\n",
+ "# Form and solve problem.\n",
+ "prob = cp.Problem(obj, constraints)\n",
+ "prob.solve()\n",
+ "\n",
+ "print(f\"status: {prob.status}\")\n",
+ "print(f\"optimal value: {prob.value:.3f}\")\n",
+ "print(f\"optimal var: x = {x.value:.3f}, y = {y.value:.3f}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true,
+ "id": "vnS1f4tUGwrj"
+ },
+ "source": [
+ "CVXPY makes it easy to change the problem formulation. For example, we can add the constraint\n",
+ "$$\n",
+ "x^2 + 2 y^2 \\leq 1\n",
+ "$$\n",
+ "and solve the problem again."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "biKaoVK9Gwrk",
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "outputId": "a0220e69-5a51-4ada-e2e9-a08909812eb2"
+ },
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "status: optimal\n",
+ "optimal value: 217.284\n",
+ "optimal var: x = 0.644, y = 0.541\n"
+ ]
+ }
+ ],
+ "source": [
+ "constraints.append(x**2+2*y**2 <= 1)\n",
+ "\n",
+ "prob = cp.Problem(obj, constraints)\n",
+ "prob.solve()\n",
+ "\n",
+ "print(f\"status: {prob.status}\")\n",
+ "print(f\"optimal value: {prob.value:.3f}\")\n",
+ "print(f\"optimal var: x = {x.value:.3f}, y = {y.value:.3f}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "QZ22NLFDGwrk"
+ },
+ "source": [
+ "What happens when we flip the inqeuality of this additional quadratic constraint? Check it out. How do you explain it?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Brief Response:** \\[Your answer here.\\]"
+ ],
+ "metadata": {
+ "id": "mcd6BVI7nK6s"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "6eRYNKK2Gwrm"
+ },
+ "source": [
+ "# An infeasible problem\n",
+ "\n",
+ "Here is a simple 2-D problem:\n",
+ "$$\n",
+ "\\begin{align}\n",
+ "\\min & \\; x+y\\\\\n",
+ "\\textrm{s.t.} &\\; x+y \\leq -5\\\\\n",
+ "&\\; x^2 + y^2 \\leq 1 \\\\\n",
+ "\\end{align}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "86YfkulPGwrm",
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "outputId": "78cafc70-ac83-41de-b288-e9ef5371d351"
+ },
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "status: infeasible\n",
+ "optimal value inf\n",
+ "optimal var None\n"
+ ]
+ }
+ ],
+ "source": [
+ "# An infeasible problem\n",
+ "x = cp.Variable()\n",
+ "y = cp.Variable()\n",
+ "\n",
+ "obj = cp.Minimize(x+y)\n",
+ "constraints = [x + y <= -5, x**2 + y**2 <= 1\n",
+ "]\n",
+ "prob = cp.Problem(obj, constraints)\n",
+ "prob.solve() # Returns the optimal value.\n",
+ "print(\"status:\", prob.status)\n",
+ "print(\"optimal value\", prob.value)\n",
+ "print(\"optimal var\", x.value)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "Can you explain the output of the solver above? What happens as you change the right hand side of the second constraint?"
+ ],
+ "metadata": {
+ "id": "PHFvdu1Rn82F"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Brief Response:** \\[Your answer here.\\]"
+ ],
+ "metadata": {
+ "id": "0kPULiFnn-9U"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "PpzGoCWgGwrm"
+ },
+ "source": [
+ "# Disciplined Convex Programming\n",
+ "\n",
+ "http://dcp.stanford.edu/home"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "Qp81k6pvGwrm"
+ },
+ "source": [
+ "# Min s-t distance\n",
+ "\n",
+ "A problem we saw in class was minimum distances. We studied a number of algorithms for different kinds of graphs; BFS for unweighted graphs, Dijkstra's algorithm for graphs with positive weights and Bellman-Ford for graphs with no negative cycles. Now we can write it as a linear program.\n",
+ "\n",
+ "First we will load [Zachary's karate club](https://en.wikipedia.org/wiki/Zachary%27s_karate_club) from Python's `networkx` library."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "iqCVs8i6Gwrm",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 516
+ },
+ "outputId": "d4f15f24-b5aa-4b19-98b2-9e1036be3e41"
+ },
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": 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\n"
+ },
+ "metadata": {}
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "import networkx as nx\n",
+ "\n",
+ "np.random.seed(2)\n",
+ "G = nx.karate_club_graph()\n",
+ "n = nx.number_of_nodes(G)\n",
+ "m = nx.number_of_edges(G)\n",
+ "pos = nx.spring_layout(G)\n",
+ "nx.draw(G, pos=pos, with_labels=True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "5m3eP3s4Gwrn"
+ },
+ "source": [
+ "We want to maximize the distance of $t$ with the constraint that we can't stretch edges.\n",
+ "\n",
+ "\\begin{align*}\n",
+ "\\max & \\; d_t \\\\\n",
+ "\\text{s.t.}\\ & |d_u - d_v| \\leq 1 &\\ \\forall \\{u, v\\} \\in E \\\\\n",
+ "& d_s = 0\n",
+ "\\end{align*}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "PX8npLBrGwrn"
+ },
+ "outputs": [],
+ "source": [
+ "distance = cp.Variable(n, nonneg=True)\n",
+ "\n",
+ "s = 0\n",
+ "t = 33\n",
+ "\n",
+ "constraints = [distance[s] == 0]\n",
+ "\n",
+ "# TODO: Formulate the constraints as above\n",
+ "...\n",
+ "\n",
+ "\n",
+ "obj = # TODO: Write the objective function\n",
+ "prob = cp.Problem(obj, constraints)\n",
+ "prob.solve()\n",
+ "print(\"status:\", prob.status)\n",
+ "print(f\"optimal value: {prob.value:.6f}\")\n",
+ "print(\"optimal values:\")\n",
+ "# for node in G:\n",
+ "# print(f\"{node:2d}: {distance[node].value:.3f}\")\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "hXJD44qqGwrn"
+ },
+ "outputs": [],
+ "source": [
+ "nx.draw(G, pos=pos, with_labels=True, node_color=distance.value / distance[t].value)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "8D43Su1NGwrn"
+ },
+ "source": [
+ "## Maximum flow\n",
+ "\n",
+ "We can also use `cvxpy` to formulate maximum flow on a graph. The constraints are that every edge cannot carry more than its capacity and except for $s$ and $t$, in all other nodes there should be flow conservation. The karate graph is undirected, but we can model each undirected $\\{u, v\\}$ edge as a pair of directed edges $(u, v)$ and $(v, u)$ going in opposite directions.\n",
+ "\n",
+ "\\begin{align*}\n",
+ "\\max & \\sum_{(v, t)} f_{(v, t)} - \\sum_{(t, v)} f_{(t, v)} \\\\\n",
+ "\\text{s.t.}\\ & 0 \\leq f_e \\leq 1, &\\ \\forall e \\in E \\\\\n",
+ "& \\sum_{(u, v)\\ \\in E} f_{(u, v)} = \\sum_{(v, w)\\ \\in E} f_{(v, w)}, &\\ \\forall v \\not \\in \\{s, t\\}\n",
+ "\\end{align*}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "UKhHkTmzGwrn"
+ },
+ "outputs": [],
+ "source": [
+ "def maxFlow(G, s, t)\n",
+ " n = nx.number_of_nodes(G)\n",
+ " m = nx.number_of_edges(G)\n",
+ "\n",
+ " edge_var = cp.Variable(2 * m) # Think of an undirected edge as two directed edges going in opposite directions\n",
+ "\n",
+ " # Note - you can organize the variables however you want after cvxpy creates them.\n",
+ " # It may make more sense to place them in 2 seperate lists based on direction. Alternatively,\n",
+ " # you can associate each one with an edge using a dictionary.\n",
+ "\n",
+ " # TODO: Write the constraints as above\n",
+ " constraints = []\n",
+ "\n",
+ " # The flow going through each edge must in [0, 1]\n",
+ "\n",
+ " # The sum of the flows going in and out of each\n",
+ " # node other than s and t must be 0\n",
+ "\n",
+ " obj = # TODO: The objective is to maximize the net flow going in to t\n",
+ " prob = cp.Problem(obj, constraints)\n",
+ " prob.solve()\n",
+ " print(\"status:\", prob.status)\n",
+ " print(\"optimal value\", prob.value)\n",
+ "\n",
+ " return prob.value\n",
+ "\n",
+ "# Test on the Karate Club graph\n",
+ "maxFlow(G, 0, 33)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "ETiQfIhcGwrn"
+ },
+ "outputs": [],
+ "source": [
+ "# Displays the graph using the results from the first m edges. Depending on how\n",
+ "# You organized your 2n variables, you may want to tweak this to get a more useful\n",
+ "# visualization. Feel free to ignore.\n",
+ "nx.draw(G, pos=pos, with_labels=True, edge_color=np.abs(edge_var.value[0:m]), edge_cmap=plt.cm.Blues)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## Linear Programming vs Dedicated Algorithms\n",
+ "\n",
+ "You already expressed $s-t$ minimum distance and maximum $s-t$ flow. If we can express these problems as LPs, then why did we spend a quarter of this class learning specific algorithms to solve them?\n",
+ "\n",
+ "In this section you will use the function you wrote on a random graph to compute maximum $s-t$ flow and then compare the running time with `networkx`'s built in Max Flow algorithm.\n",
+ "\n",
+ "First you need to create a $G(n, p)$ graph and then find the maximum flow between nodes $0$ and $n-1$."
+ ],
+ "metadata": {
+ "id": "mlPWUokEJdgt"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "n = 100\n",
+ "p = 2 * n * np.log(n)\n",
+ "Gnp = nx.fast_gnp_random_graph(n, p)\n",
+ "nx.set_edge_attributes(Gnp, 1, 'capacity')\n",
+ "\n",
+ "%timeit flow = maxFlow(Gnp, 0, n - 1)\n",
+ "%timeit flow = nx.maximum_flow_value(Gnp, 0, n - 1)"
+ ],
+ "metadata": {
+ "id": "IFLmKOuBJcdv"
+ },
+ "execution_count": null,
+ "outputs": []
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "The fraction of time taken between Linear Programming and `networkx` is: [**TODO**: Your answer here.]"
+ ],
+ "metadata": {
+ "id": "GPQWZcipsnqi"
+ }
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
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+ "codemirror_mode": {
+ "name": "ipython",
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+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.6"
+ },
+ "latex_envs": {
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+ "hotkeys": {
+ "equation": "Ctrl-E",
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+ "colab": {
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+ "nbformat": 4,
+ "nbformat_minor": 0
+}
\ No newline at end of file