EECS227C-HW2 Code

Q1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import cvxpy as cvx\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.zeros((5,10,10))\n",
    "b = np.zeros((5,10))\n",
    "\n",
    "for k in range(5):\n",
    "    for i in range(10):\n",
    "        for j in range(10):\n",
    "            if i < j:\n",
    "                A[k,i,j] = np.exp((i+1)/(j+1))*np.cos((i+1)*(j+1))*np.sin(k+1)\n",
    "            elif j < i :\n",
    "                A[k,i,j] = np.exp((j+1)/(i+1))*np.cos((i+1)*(j+1))*np.sin(k+1)\n",
    "            else:\n",
    "                A[k,i,j] = 0 \n",
    "\n",
    "\n",
    "for k in range(5):\n",
    "    for i in range(10):\n",
    "        b[k,i] = np.exp((i+1)/(k+1))*np.sin((i+1)*(k+1))\n",
    "        A[k,i,i] = ((i+1)/10)*np.abs(np.sin(k+1)) + np.sum(np.abs(A[k,i,:]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    ct = -100000\n",
    "    arg =  None\n",
    "    #mult = False\n",
    "\n",
    "    for k in range(5):\n",
    "        if x.T@A[k]@x-x.T@b[k] == ct:\n",
    "            #mult = True\n",
    "            arg = k \n",
    "\n",
    "        if x.T@A[k]@x-x.T@b[k] > ct :\n",
    "            #mult = False\n",
    "            arg = k\n",
    "            ct = x.T@A[k]@x-x.T@b[k]\n",
    "\n",
    "    return ct, 2*(A[arg]@x)-b[arg]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (a) f(x0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5337.066429311364"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = np.ones(10)\n",
    "f(x0)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.8414083346162645 [-0.12625655 -0.03437833 -0.00685703  0.02636084  0.06729451 -0.27839957\n",
      "  0.07421914  0.13852438  0.08403105  0.03858013]\n"
     ]
    }
   ],
   "source": [
    "x = cvx.Variable(10)\n",
    "z = cvx.Variable(1)\n",
    "\n",
    "\n",
    "objective = cvx.Minimize(z)\n",
    "constraints = []\n",
    "for i in range(5):\n",
    "    constraints.append(cvx.quad_form(x,A[i]) - x.T@b[i] <= z)\n",
    "    \n",
    "p = cvx.Problem(objective, constraints)\n",
    "primal_result = p.solve()\n",
    "print(primal_result,x.value)\n",
    "\n",
    "opt = primal_result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Level Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.8/site-packages/cvxpy/problems/problem.py:1296: UserWarning: Solution may be inaccurate. Try another solver, adjusting the solver settings, or solve with verbose=True for more information.\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.5\n",
    "steps = 1000#1e4\n",
    "\n",
    "t=1\n",
    "xt = x0\n",
    "mins = f(x0)[0]\n",
    "\n",
    "vals = []\n",
    "fL = []\n",
    "fU = []\n",
    "arr = []\n",
    "\n",
    "term = False\n",
    "\n",
    "Bound = 1e2\n",
    "\n",
    "x = cvx.Variable(10)\n",
    "z = cvx.Variable(1)\n",
    "objective = cvx.Minimize(z)\n",
    "constraints = []\n",
    "constraints.append(cvx.norm(x,2)<= Bound)\n",
    "\n",
    "while t < steps:\n",
    "    val,grad = f(xt)    \n",
    "    vals.append(val)\n",
    "    \n",
    "    constraints.append(val + grad@(x-xt) <= z)\n",
    "    p = cvx.Problem(objective, constraints)\n",
    "    p.solve()\n",
    "    primal_result = p.value\n",
    "    \n",
    "    fL.append(primal_result)\n",
    "    fU.append(min(vals))\n",
    "    Lt = (1-alpha)*fL[-1]+alpha*fU[-1] \n",
    "\n",
    "    ## Projection\n",
    "    obj = cvx.Minimize(cvx.norm(x-xt,2))\n",
    "    const = constraints.copy()\n",
    "    const.append(z == Lt)\n",
    "    p = cvx.Problem(obj, const)\n",
    "    try:\n",
    "        p.solve()\n",
    "        nxt = x.value\n",
    "    except:\n",
    "        term = True\n",
    "    \n",
    "    if term:\n",
    "        break\n",
    "        \n",
    "    arr.append(fU[-1]-opt)\n",
    "    t += 1\n",
    "    xt = nxt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(arr)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(arr)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "40d3a090f54c6569ab1632332b64b2c03c39dcf918b08424e98f38b5ae0af88f"
  },
  "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

Q2.ipynb