Barrier Method.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "a_kT8ijD88LD"
   },
   "source": [
    "# Barrier Method for Quadratic Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "AUdvKNzD9Lek"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import cvxpy as cp\n",
    "from scipy.linalg import hilbert\n",
    "from scipy.sparse import diags\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Qj3-0dzkOQhu"
   },
   "source": [
    "## Writing the objective function\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ccLTWpZC9dLI"
   },
   "outputs": [],
   "source": [
    "def h(x, q, P):\n",
    "    return np.dot(P, x) - q\n",
    "\n",
    "def phi(x, q, P):\n",
    "    return -np.sum(np.log(-h(x, q, P)))\n",
    "\n",
    "def quad(x, A, b):\n",
    "    return np.dot(x, np.dot(A, x)) / 2 - np.dot(b, x)\n",
    "\n",
    "def f(x, A, b, q, P, t):\n",
    "    return t * quad(x, A, b) + phi(x, q, P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "NKrDJaFGdOgp"
   },
   "source": [
    "## Defining the gradients\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Xh-bDAiNSLbh"
   },
   "outputs": [],
   "source": [
    "def phi_grad(x, q, P):\n",
    "    return np.sum((P.T / (-h(x, q, P))).T, 0)\n",
    "\n",
    "def quad_grad(x, A, b):\n",
    "    return np.dot(A, x) - b\n",
    "\n",
    "def f_grad(x, A, b, q, P, t):\n",
    "    return t * quad_grad(x, A, b) + phi_grad(x, q, P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7UkQFtW4rLWo"
   },
   "source": [
    "## Defining the hessians and inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "xlz8uaYnrRU7"
   },
   "outputs": [],
   "source": [
    "def phi_hessian(x, q, P):\n",
    "    n = len(x)\n",
    "    res = np.zeros((n, n))\n",
    "    for i in range(n):\n",
    "        res += np.matmul(P[i].T, P[i]) / (q[i]-np.dot(P[i],x))**2\n",
    "    return res\n",
    "\n",
    "def f_hessian(x, A, b, q, P, t):\n",
    "    return t*A + phi_hessian(x, q, P)\n",
    "\n",
    "def f_hessian_inv(x, A, b, q, P, t):\n",
    "    return np.linalg.inv(f_hessian(x, A, b, q, P, t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ABFLFnMDDtXW"
   },
   "source": [
    "## Find starting point using **CVXPY**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "OlJX2N6jDz_K"
   },
   "outputs": [],
   "source": [
    "def find_feasible(q, P):\n",
    "    n = len(q)\n",
    "    x = cp.Variable((n))\n",
    "    s = cp.Variable((1))\n",
    "\n",
    "    constraints = [cp.max(P @ x - q) <= s, s <= 0]\n",
    "    obj = cp.Maximize(s)\n",
    "    prob = cp.Problem(obj, constraints)\n",
    "    prob.solve()\n",
    "    return x.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PKCHLV3hDTo-"
   },
   "source": [
    "## Defining Newton and barrier methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "QbTWzXWA4VDj"
   },
   "outputs": [],
   "source": [
    "def newton(x, A, b, q, P, t, beta, alpha, max_iter, eps):\n",
    "    i = 0\n",
    "    \n",
    "    while i < max_iter:\n",
    "        i += 1\n",
    "        s = 1\n",
    "        fx = f(x, A, b, q, P, t)\n",
    "        gradient = f_grad(x, A, b, q, P, t)\n",
    "        hessian_inv = f_hessian_inv(x, A, b, q, P, t)\n",
    "        v = -np.matmul(hessian_inv, gradient)\n",
    "        lambd = -np.matmul(gradient, v)\n",
    "        \n",
    "        if lambd / 2 <= eps:\n",
    "            break\n",
    "        \n",
    "        while np.amax(h(x + s*v, q, P)) >= 0:\n",
    "            s *= beta\n",
    "\n",
    "        while True:\n",
    "            new_x = x + s*v\n",
    "            new_f = f(new_x, A, b, q, P, t)\n",
    "            \n",
    "            if new_f <= fx - alpha * s * lambd:\n",
    "                break\n",
    "            s *= beta\n",
    "            \n",
    "        if fx == new_f:\n",
    "            break\n",
    "    \n",
    "        x = new_x\n",
    "            \n",
    "    gradient = f_grad(x, A, b, q, P, t)\n",
    "    hessian_inv = f_hessian_inv(x, A, b, q, P, t)\n",
    "    v = -np.matmul(hessian_inv, gradient)\n",
    "    lambd = -np.matmul(gradient, v)\n",
    "\n",
    "    return x, i, lambd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "SuOBDoRPuRje"
   },
   "outputs": [],
   "source": [
    "def barrier(x, A, b, q, P, beta, alpha, max_iter, eps, mu):\n",
    "    iters = []\n",
    "    gap = []\n",
    "    obj = []\n",
    "    iter_sum = 0\n",
    "    n = len(x)\n",
    "    t = 1\n",
    "    \n",
    "    while n/t > eps:\n",
    "        x, i, lambd = newton(x, A, b, q, P, t, beta, alpha, max_iter, eps)\n",
    "        iter_sum += i\n",
    "        iters.append(iter_sum)\n",
    "        gap.append(n/t)\n",
    "        obj.append(quad(x, A, b))\n",
    "        t *= mu\n",
    "\n",
    "    return x, gap, iters, obj"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "i53CCoxQDTpL"
   },
   "source": [
    "## Constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Ad2AiKwuvoVW"
   },
   "outputs": [],
   "source": [
    "beta = 0.5\n",
    "alpha = 0.01\n",
    "max_iter = 20\n",
    "eps = 1e-3\n",
    "mus = [1.5, 3, 5, 10]\n",
    "sizes = [100, 400]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "o0BJg7pWDTpT"
   },
   "source": [
    "## Initialization function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "2S4RCKffDTpU"
   },
   "outputs": [],
   "source": [
    "def init(n):\n",
    "    P = np.random.normal(size = (n, n))\n",
    "    q = np.random.normal(size = n)\n",
    "    b = np.ones(n)\n",
    "    t = 1\n",
    "    return P, q, b, t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Xl4cBKs2DTpX"
   },
   "source": [
    "## Experiments on tridiagonal matrices: tridiag(-1, 4, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "auCqLEB8DTpY"
   },
   "outputs": [],
   "source": [
    "def get_tridiag(n):\n",
    "    return init(n), diags([-1, 4, -1], [-1, 0, 1], shape=(n, n)).toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 783
    },
    "colab_type": "code",
    "id": "OV25i1HkDTpf",
    "outputId": "557d855a-b73a-4743-b22a-1df990dad9ca"
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for n in sizes:\n",
    "    (P, q, b, t), A = get_tridiag(n)\n",
    "    x = find_feasible(q, P)\n",
    "    \n",
    "    plt.style.use('seaborn-whitegrid')\n",
    "    plt.figure(figsize=(9, 6))\n",
    "    plt.title(\"Duality gap for tridiagonal matrix with size {} * {}\".format(n, n))\n",
    "    plt.xlabel(\"Newton Iterations\")\n",
    "    plt.ylabel(\"Duality gap\")\n",
    "    \n",
    "    for mu in mus:\n",
    "        x, gap, iters, obj = barrier(x, A, b, q, P, beta, alpha, max_iter, eps, mu)\n",
    "        plt.step(iters, gap, label='mu ({})'.format(mu))\n",
    "        \n",
    "    plt.yscale('log')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Vzr3UunPDTpm"
   },
   "source": [
    "## Experiments on Hilbert matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 783
    },
    "colab_type": "code",
    "id": "XfNdiOznwolO",
    "outputId": "a1464579-d52c-41bb-9c16-847cd35c243f"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for n in sizes:\n",
    "    A = hilbert(n)\n",
    "    P, q, b, t = init(n)\n",
    "    x = find_feasible(q, P)\n",
    "    \n",
    "    plt.style.use('seaborn-whitegrid')\n",
    "    plt.figure(figsize=(9, 6))\n",
    "    plt.title(\"Duality gap for Hilbert matrix with size {} * {}\".format(n, n))\n",
    "    plt.xlabel(\"Newton Iterations\")\n",
    "    plt.ylabel(\"Duality gap\")\n",
    "    \n",
    "    for mu in mus:\n",
    "        x, gap, iters, obj = barrier(x, A, b, q, P, beta, alpha, max_iter, eps, mu)\n",
    "        plt.step(iters, gap, label='mu ({})'.format(mu))\n",
    "        \n",
    "    plt.yscale('log')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "CVXHW4P4.ipynb",
   "provenance": [],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}