demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "1zH3z99DdpMn"
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "uofC2Sg5dpMo"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from LPSolver import LPSolver\n",
    "from QPSolver import QPSolver\n",
    "from SOCPSolver import SOCPSolver\n",
    "from LassoSolver import LassoSolver\n",
    "import cvxpy as cp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "id": "04Mn5K9tdpMo"
   },
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sfx96ozadpMp"
   },
   "source": [
    "### Generate a feasible problem instance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "id": "fxBx8mVJdpMq"
   },
   "outputs": [],
   "source": [
    "m = 80  # number of equality constraints -- keep lower than number of variables to ensure there are multiple solutions to the problem\n",
    "n = 100  # number of variables\n",
    "\n",
    "A = rng.normal(size = (m,n))\n",
    "\n",
    "random_row_index = np.random.choice(m)\n",
    "\n",
    "# Set all entries in the selected row to their absolute values\n",
    "A[random_row_index, :] = np.abs(A[random_row_index, :])\n",
    "\n",
    "b = A@np.abs(rng.normal(size = (n,)))\n",
    "c = rng.normal(size = (n,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WF8SbBE5dpMq"
   },
   "source": [
    "### Create a LPSolver object"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QdgQG5cfdpMq"
   },
   "source": [
    "Can specify use_gpu = True if you want to run with a GPU. GPU solver typically starts to surpass performance of CPU solver ~500 variables (depending on system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "S3tHWDxydpMr"
   },
   "source": [
    "Also able to make multiple instances of this object to compare different hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "id": "2NKG6JwndpMr"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Not able to run with GPU\n",
      "Testing CVXPY\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\"Initialize LP problem of form:\n",
    "        Minimize c^T x\n",
    "        Subject to Ax == b\n",
    "                   Cx <= d\n",
    "                   lower_bound <= x <= upper_bound\n",
    "\n",
    "Can leave A, b, C, d, and c as None or specify matrices/vectors to constrain the problem\n",
    "\"\"\"\n",
    "\n",
    "ls= LPSolver(c=c,\n",
    "        A=A,\n",
    "        b=b,\n",
    "        C=None,\n",
    "        d=None,\n",
    "        use_gpu=False,\n",
    "        upper_bound=3,\n",
    "        lower_bound=0,\n",
    "        update_slacks_every=5,\n",
    "        suppress_print=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sPZcznzIdpMs"
   },
   "source": [
    "#### Compare LPSolver solution to the CVXPY solution\n",
    "Check the ls.value parameter if you want to extract the value of the solution, use ls.xstar to get the minimizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "id": "AlXgX0_QdpMs",
    "outputId": "4a8d4318-33f1-4966-c579-dba71135cf34"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "proceeding to solve method\n",
      "Objective value is now -7.821270181214127\n",
      "Objective value is now -9.056109597164873\n",
      "Objective value is now -13.795599994280783\n",
      "Objective value is now -14.648400867663327\n",
      "Objective value is now -14.705223388749173\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -14.708923873448619\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -14.70916981482835\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -14.709185929948589\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -14.709209564370934\n",
      "REACHED MAX ITERATIONS: Problem likely infeasible or unbounded (Likely infeasible)\n",
      "Objective value is now -14.709133349083984\n",
      "Reached max Newton steps during 10th centering step (t=3844335937.5)\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Newton step at iteration 11 did not converge\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Newton step at iteration 12 did not converge\n",
      "REACHED MAX ITERATIONS: Problem likely infeasible or unbounded (Likely infeasible)\n",
      "Newton step at iteration 13 did not converge\n",
      "Reached max Newton steps during 13th centering step (t=12974633789062.5)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-2.2267986357960012e-05"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls.solve(track_loss=True) - ls.cvxpy_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Convergence of LPSolver'}, xlabel='Cumulative Newton iterations', ylabel='Optimality gap'>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ls.plot() # the algorithm quit once the objective value stopped decreasing (which may happen in equality constrained problems)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xMYz9WmKdpMt"
   },
   "source": [
    "### Benchmark LPSolver times vs. CVXPY\n",
    "Can also generate multiple instances of LP to benchmark times of different hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "YNoiYvtzdpMt",
    "outputId": "87587a60-39bc-44cf-b2a8-80f7c12ba8ff"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.71 s ± 40.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "x = cp.Variable(len(c))\n",
    "obj = cp.Minimize(c.T@x)\n",
    "constr = [A@x == b,\n",
    "        x <= 0]\n",
    "prob = cp.Problem(obj, constr)\n",
    "prob.solve(solver='CLARABEL')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "1ut06GKedpMt",
    "outputId": "51c7f462-64a2-4cbb-d03a-a3735e2013c3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.03 s ± 3.97 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit ls.solve(resolve=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "Ag6ytWh9dpMu",
    "outputId": "e3fd9077-68bc-429a-ee1f-e78bff17f573"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "250 ms ± 1.86 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit ls_gpu.solve(resolve=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "rpB-ZZOHdpMu",
    "outputId": "65b42cbb-c042-4899-b6e5-fadb5a99fd83"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Convergence of LPSolver'}, xlabel='Cumulative Newton iterations', ylabel='Optimality gap'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ls_gpu.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Try out an inequality constrained problem (solver will run phase 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Not able to run with GPU\n",
      "Not able to run with GPU\n"
     ]
    }
   ],
   "source": [
    "n = 100\n",
    "m = 50\n",
    "C = np.random.random((m,n))\n",
    "C = np.where(np.random.binomial(1, 0.10, C.shape), C, 0)  # <- apply a random mask with 10% density  (A will be 90% sparse)\n",
    "d = np.random.randint(low=1, high=30, size=C.shape[0])\n",
    "\n",
    "c = np.random.randint(low=1, high=n, size=C.shape[1]) - n/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing CVXPY\n",
      "Starting slack of 5.9864\n"
     ]
    }
   ],
   "source": [
    "# provide an x0 to force the solver to complete phase 1 solve\n",
    "\n",
    "ls= LPSolver(c=c,\n",
    "        A=A,\n",
    "        b=b,\n",
    "        C=C,\n",
    "        d=d,\n",
    "        use_gpu=False,\n",
    "        upper_bound=None,\n",
    "        lower_bound=0,\n",
    "        suppress_print=False,\n",
    "        epsilon=1e-10,\n",
    "        t0=1,\n",
    "        update_slacks_every=5,\n",
    "        x0=np.ones(len(c)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "running phase 1 solver\n",
      "Current slack: 5.98635554133264\n",
      "Current slack: 14996.304442001596\n",
      "Current slack: 997.1863898023126\n",
      "Current slack: 64.07406255477198\n",
      "Current slack: 2.6033319649533615\n",
      "found a feasible point with slack -0.22639232027039274\n",
      "proceeding to solve method\n",
      "Objective value is now -8541.665643336326\n",
      "Objective value is now -8632.511509201697\n",
      "Objective value is now -8638.664775554995\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -8639.075412302309\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -8639.102790126659\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -8639.104614067735\n",
      "Cholesky solver failed due to numeric instability. Proceeding with Numpy solve...\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -8639.104803633845\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -8639.10474560794\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -8639.104745480483\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -8639.104745495471\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -8639.104745495488\n",
      "REACHED MAX ITERATIONS: Problem likely infeasible or unbounded (Likely unbounded)\n",
      "Objective value is now -8639.10474549549\n",
      "Reached max Newton steps during 12th centering step (t=8649755859375)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-5.82852226216346e-05"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls.solve() - ls.cvxpy_val"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Run the same problem, but turn it into a QP by passing the identity matrix to P in QPSolver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing CVXPY\n",
      "Starting slack of 78.7609\n"
     ]
    }
   ],
   "source": [
    "# Also add in a dummy equality constraint just to showcase capability\n",
    "# for example, here we are forcing the first entry in x to be 1\n",
    "A = np.hstack((1, np.zeros(len(c)-1))).reshape(1,-1)\n",
    "b = np.array([1])\n",
    "\n",
    "qs= QPSolver(P=np.eye(len(c)), \n",
    "        q=c,\n",
    "        A=A,\n",
    "        b=b,\n",
    "        C=C,\n",
    "        d=d,\n",
    "        t0=0.1,\n",
    "        use_gpu=False,\n",
    "        upper_bound=None,\n",
    "        lower_bound=0,\n",
    "        suppress_print=False,\n",
    "        mu=15,\n",
    "        x0 = np.ones(len(c))*10,\n",
    "        update_slacks_every=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "running phase 1 solver\n",
      "Current slack: 78.76085151472293\n",
      "Current slack: 14996.928601058991\n",
      "Current slack: 997.1866137531274\n",
      "Current slack: 64.07406263767669\n",
      "Current slack: 2.6033319649561926\n",
      "found a feasible point with slack -0.22639232027036854\n",
      "proceeding to solve method\n",
      "Objective value is now -4620.589435840365\n",
      "Objective value is now -5316.442786746958\n",
      "Objective value is now -5370.8392221072345\n",
      "Objective value is now -5374.525486524601\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -5374.746225631481\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -5374.788549248652\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -5374.789538351915\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -5374.789722506872\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -5374.789725911084\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -5374.7897277163665\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -5374.789727731493\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -5374.789727739523\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -5374.789727739608\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-1.0571115126367658e-05"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qs.solve(track_loss=True) - qs.cvxpy_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Convergence of QPSolver'}, xlabel='Cumulative Newton iterations', ylabel='Optimality gap'>"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qs.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SOCP Solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load in data from HW5\n",
    "\n",
    "LAMBDA = 0.02\n",
    "RHO = 0.4\n",
    "T = 10\n",
    "GROUPS = [\n",
    "    [0],\n",
    "    [1],\n",
    "    [2],\n",
    "    [3, 4, 5, 6, 7],\n",
    "    [8, 9, 10, 11, 12, 13],\n",
    "    [14, 15],\n",
    "    [16],\n",
    "    [17],\n",
    "    [18],\n",
    "]\n",
    "FSTAR = 49.9649387126726\n",
    "\n",
    "def get_weights(groups):\n",
    "\n",
    "    group_sizes = list(map(len, groups))\n",
    "    weights = np.sqrt(group_sizes)\n",
    "    return weights\n",
    "\n",
    "def load_data(X_train_path, y_train_path):\n",
    "    X_train = np.loadtxt(X_train_path, delimiter=\",\")\n",
    "    X_train = np.hstack([np.ones(X_train.shape[0])[:, np.newaxis], X_train])\n",
    "    y_train = np.loadtxt(y_train_path, delimiter=\",\")\n",
    "    return X_train, y_train\n",
    "\n",
    "X, Y = load_data('example_data/X_train.csv', 'example_data/Y_train.csv')\n",
    "w = get_weights(GROUPS)[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "# transform into format for SOCPSolver\n",
    "\n",
    "P = np.zeros((27,27))\n",
    "P[:19,:19] = 1/(X.shape[0]) * X.T@X\n",
    "q = np.zeros(27)\n",
    "q[:19] = -1/(X.shape[0]) * Y.T@X\n",
    "q[19:] = LAMBDA * w\n",
    "A = []\n",
    "c = []\n",
    "for i in range(len(GROUPS)-1):\n",
    "    Ai = np.zeros((27,27))\n",
    "    ci = np.zeros(27)\n",
    "    Ai[GROUPS[i+1], GROUPS[i+1]] = 1\n",
    "    A.append(Ai)\n",
    "    ci[i+19] = 1\n",
    "    c.append(ci)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing CVXPY\n",
      "Starting slack of 2.969\n"
     ]
    }
   ],
   "source": [
    "scs = SOCPSolver(P=P, \n",
    "        q=q,\n",
    "        A=A,\n",
    "        b=None,\n",
    "        c=c,\n",
    "        d=None,\n",
    "        use_gpu=False,\n",
    "        upper_bound=None,\n",
    "        lower_bound=None,\n",
    "        suppress_print=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Currently running into occasional bug where phase 1 solver converges to small positive number!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "running phase 1 solver\n",
      "Current slack: 2.968956478616826\n",
      "Cholesky solver failed due to numeric instability. Proceeding with Numpy solve...\n",
      "found a feasible point with slack -242.59279408119625\n",
      "proceeding to solve method\n",
      "REACHED MAX ITERATIONS: Problem likely infeasible or unbounded (Likely infeasible)\n",
      "Objective value is now -270.9968954680217\n",
      "Reached max Newton steps during 1th centering step (t=0.1)\n",
      "Objective value is now -418.3762764785082\n",
      "Objective value is now -427.189927748653\n",
      "Objective value is now -427.6315154356971\n",
      "Objective value is now -427.65697057132735\n",
      "Objective value is now -427.6586333162318\n",
      "Objective value is now -427.6587440266498\n",
      "Objective value is now -427.65875141953455\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -427.6587518477065\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -427.65875184974743\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -427.6587518500406\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -427.65875185004023\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3.5586822377808858e-09"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scs.solve() - scs.cvxpy_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(49.96493879693293, 49.9649387126726)"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# confirm that we get the same solution as in the homework\n",
    "\n",
    "scs.value + Y.T@Y/(2*X.shape[0]), FSTAR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random problem generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 10\n",
    "n = 50\n",
    "p = 10\n",
    "n_i = 15\n",
    "f = np.random.randn(n)\n",
    "A = []\n",
    "b = []\n",
    "c = []\n",
    "d = []\n",
    "x0 = np.random.randn(n)\n",
    "for i in range(m):\n",
    "    A.append(np.random.randn(n_i, n))\n",
    "    b.append(np.random.randn(n_i))\n",
    "    c.append(np.random.randn(n))\n",
    "    d.append(np.linalg.norm(A[i] @ x0 + b[i], 2) - c[i].T @ x0)\n",
    "F = np.random.randn(p, n)\n",
    "g = F @ x0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing CVXPY\n",
      "Starting slack of 861.9187\n"
     ]
    }
   ],
   "source": [
    "scs = SOCPSolver(P=None, \n",
    "        q=f,\n",
    "        A=A,\n",
    "        b=b,\n",
    "        c=c,\n",
    "        d=d,\n",
    "        F=None,\n",
    "        g=None,\n",
    "        use_gpu=False,\n",
    "        upper_bound=None,\n",
    "        lower_bound=None,\n",
    "        suppress_print=False,\n",
    "        update_slacks_every=0,\n",
    "        check_cvxpy=True,\n",
    "        alpha=0.02,\n",
    "        x0=np.ones(len(f))*1)\n",
    "\n",
    "#scs.solve(track_loss=True) - scs.cvxpy_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "running phase 1 solver\n",
      "Current slack: 861.9187066433233\n",
      "found a feasible point with slack -81.72190907530921\n",
      "proceeding to solve method\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -64.587393885886\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -112.57500020632511\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -117.48027444243709\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -118.36416778880648\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -118.38082392636395\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -118.40665911644221\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -118.41737793287118\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -118.41925843889183\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -118.4199376329336\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -118.42010066511388\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -118.42016365993258\n",
      "Backtracking search got stuck, returning from Newton's method now...\n",
      "Objective value is now -118.42017380175723\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.6654780552016746e-05"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scs.solve(track_loss=True) - scs.cvxpy_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Convergence of SOCPSolver'}, xlabel='Cumulative Newton iterations', ylabel='Optimality gap'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scs.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Benchmark SOCP Solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "scs = SOCPSolver(P=None, \n",
    "        q=f,\n",
    "        A=A,\n",
    "        b=b,\n",
    "        c=c,\n",
    "        d=d,\n",
    "        F=F,\n",
    "        g=g,\n",
    "        use_gpu=False,\n",
    "        upper_bound=None,\n",
    "        lower_bound=None,\n",
    "        suppress_print=True,\n",
    "        update_slacks_every=0,\n",
    "        check_cvxpy=False)\n",
    "\n",
    "#scs.solve(track_loss=True) - scs.cvxpy_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/frankdeguire/anaconda3/envs/ee364/lib/python3.11/site-packages/cvxpy/reductions/solvers/solving_chain.py:336: FutureWarning: \n",
      "    Your problem is being solved with the ECOS solver by default. Starting in \n",
      "    CVXPY 1.5.0, Clarabel will be used as the default solver instead. To continue \n",
      "    using ECOS, specify the ECOS solver explicitly using the ``solver=cp.ECOS`` \n",
      "    argument to the ``problem.solve`` method.\n",
      "    \n",
      "  warnings.warn(ECOS_DEPRECATION_MSG, FutureWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.4 s ± 3.32 s per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "# Define and solve the CVXPY problem.\n",
    "x = cp.Variable(n)\n",
    "# We use cp.SOC(t, x) to create the SOC constraint ||x||_2 <= t.\n",
    "soc_constraints = [\n",
    "      cp.SOC(c[i].T @ x + d[i], A[i] @ x + b[i]) for i in range(m)\n",
    "]\n",
    "prob = cp.Problem(cp.Minimize(f.T@x),\n",
    "                  soc_constraints + [F @ x == g])\n",
    "prob.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.89 s ± 355 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit scs.solve(track_loss=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1298.4653910738707, -1298.4653972079934)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob.value, scs.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Convergence of SOCPSolver'}, xlabel='Cumulative Newton iterations', ylabel='Optimality gap'>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scs.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LassoSolver"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Our true winnner)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate random problem data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate a sparse x so that it replicates a LASSO problem well. Generate multiple problem instances by generating a B matrix instead of just a vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "id": "fCW0MxC9dpMu"
   },
   "outputs": [],
   "source": [
    "m = 500\n",
    "n = 150\n",
    "num_problems = 30\n",
    "num_nonzero = 1000 # create a sparse x_true with this many nonzero entries\n",
    "A = np.random.rand(m, n)\n",
    "x_true = np.zeros((n, num_problems))\n",
    "x_true[np.unravel_index(np.random.randint(0,n*num_problems, num_nonzero), (n, num_problems))] = np.random.uniform(0,50, num_nonzero)\n",
    "reg = 0.05 + 0.01*np.random.randn(num_problems) # give each subproblem a slightly different regularization\n",
    "B = A@x_true + np.random.randn(m, num_problems)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing CVXPY\n",
      "CVXPY solving sample 1...Optimal value of 8.5134\n",
      "CVXPY solving sample 2...Optimal value of 15.3696\n",
      "CVXPY solving sample 3...Optimal value of 6.7719\n",
      "CVXPY solving sample 4...Optimal value of 13.7393\n",
      "CVXPY solving sample 5...Optimal value of 14.8268\n",
      "CVXPY solving sample 6...Optimal value of 11.2279\n",
      "CVXPY solving sample 7...Optimal value of 13.0617\n",
      "CVXPY solving sample 8...Optimal value of 7.5663\n",
      "CVXPY solving sample 9...Optimal value of 8.452\n",
      "CVXPY solving sample 10...Optimal value of 11.3587\n",
      "CVXPY solving sample 11...Optimal value of 9.579\n",
      "CVXPY solving sample 12...Optimal value of 14.5551\n",
      "CVXPY solving sample 13...Optimal value of 16.4474\n",
      "CVXPY solving sample 14...Optimal value of 18.2706\n",
      "CVXPY solving sample 15...Optimal value of 12.8363\n",
      "CVXPY solving sample 16...Optimal value of 9.7036\n",
      "CVXPY solving sample 17...Optimal value of 12.2318\n",
      "CVXPY solving sample 18...Optimal value of 15.5859\n",
      "CVXPY solving sample 19...Optimal value of 11.9294\n",
      "CVXPY solving sample 20...Optimal value of 11.9577\n",
      "CVXPY solving sample 21...Optimal value of 12.542\n",
      "CVXPY solving sample 22...Optimal value of 11.1823\n",
      "CVXPY solving sample 23...Optimal value of 10.1845\n",
      "CVXPY solving sample 24...Optimal value of 11.1099\n",
      "CVXPY solving sample 25...Optimal value of 14.034\n",
      "CVXPY solving sample 26...Optimal value of 8.9551\n",
      "CVXPY solving sample 27...Optimal value of 13.0326\n",
      "CVXPY solving sample 28...Optimal value of 7.3535\n",
      "CVXPY solving sample 29...Optimal value of 8.6678\n",
      "CVXPY solving sample 30...Optimal value of 6.9143\n"
     ]
    }
   ],
   "source": [
    "# create the LassoSolver object to solve all subproblems in parallel\n",
    "# add the bias term and normalize A and then compare to CVXPY solver\n",
    "\n",
    "ls = LassoSolver(\n",
    "        A,\n",
    "        B,\n",
    "        reg=reg,\n",
    "        rho=0.4,\n",
    "        max_iters=1000,\n",
    "        check_stop=10,\n",
    "        add_bias=True,\n",
    "        normalize_A=True,\n",
    "        positive=False,\n",
    "        compute_loss=True,\n",
    "        adaptive_rho=False,\n",
    "        eps_abs=1e-6,\n",
    "        eps_rel=1e-4,\n",
    "        use_gpu=False,\n",
    "        num_chunks=0\n",
    "    )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, solutions, gaps, iters = ls.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.02998526, -0.02605976, -0.00041404, -0.0524055 , -0.05616224,\n",
       "       -0.01734689, -0.04153745, -0.00364761, -0.03187835, -0.02356449,\n",
       "       -0.01958842, -0.03259362, -0.04862576, -0.05271794, -0.06422837,\n",
       "       -0.01690379, -0.0262829 , -0.06294509, -0.01991161, -0.02811559,\n",
       "       -0.02073896, -0.02931188, -0.01732493, -0.02096987, -0.02420308,\n",
       "       -0.03021745, -0.06417266, -0.00821221, -0.00873121, -0.00733874])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# LassoSolver actually achieved lower objective values than CVXPY!\n",
    "solutions - ls.cvxpy_vals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Convergence of LassoSolver'}, xlabel='iteration number', ylabel='Optimality gap'>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# note that, because LassoSolver achieved better objective values than CVXPY, the optimal value was considered the value at the end of the LassoSolver solve, which is why\n",
    "# the optimality gap goes to negative infinity on the log plot\n",
    "ls.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Benchmark against CVXPY\n",
    "#### One good use case of solving multiple problems in parallel is being able to test several regularization strengths at the same time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate data\n",
    "# have one vector for b (only solving one problem instance), but generate multiple values for regularization strength\n",
    "# test 50 different regularization strengths logarithmically spaced from 10^-5 to 10^2\n",
    "\n",
    "m = 800\n",
    "n = 400\n",
    "num_problems = 1\n",
    "num_nonzero = 10000 # create a sparse x_true with this many nonzero entries\n",
    "A = np.random.rand(m, n)\n",
    "x_true = np.zeros((n, num_problems))\n",
    "x_true[np.unravel_index(np.random.randint(0,n*num_problems, num_nonzero), (n, num_problems))] = np.random.uniform(0,50, num_nonzero)\n",
    "reg = np.logspace(-5,2,50)\n",
    "b = A@x_true + np.random.randn(m, num_problems)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create the LassoSolver object to solve all subproblems in parallel\n",
    "# turn off compute loss and lower epsilons a bit (resort to defauly -- we were already outperforming CVXPY anyways)\n",
    "# add a bias term, but don't normalize A here\n",
    "\n",
    "ls = LassoSolver(\n",
    "        A,\n",
    "        b,\n",
    "        reg=reg,\n",
    "        rho=0.004,\n",
    "        max_iters=10000,\n",
    "        check_stop=100,\n",
    "        add_bias=True,\n",
    "        normalize_A=False,\n",
    "        positive=False,\n",
    "        compute_loss=False,\n",
    "        adaptive_rho=False,\n",
    "        use_gpu=True,\n",
    "        num_chunks=0,\n",
    "        eps_rel=1e-6,\n",
    "    eps_abs=1e-6,\n",
    "        check_cvxpy=False\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "57.54086780548096\n"
     ]
    }
   ],
   "source": [
    "# time how long it takes to solve all the problems in CVXPY (we must solve sequentially)\n",
    "from time import time\n",
    "vals = []\n",
    "A = np.hstack((np.ones((m,1)), A))\n",
    "start = time()\n",
    "for r in reg:\n",
    "    x = cp.Variable(n+1)\n",
    "    obj = cp.Minimize(1/(2*m)*cp.norm2(A@x - b[:,0])**2 + r*cp.norm(x[1:], 1))\n",
    "    prob = cp.Problem(obj, [])\n",
    "    prob.solve(solver='CLARABEL')\n",
    "    vals.append(prob.value)\n",
    "print(time()-start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.03676304e-06,  2.48952755e-06,  2.80171960e-06,  2.62359206e-06,\n",
       "        1.19473962e-06,  1.06894333e-07,  2.05324122e-08,  4.18690793e-09,\n",
       "        3.55764307e-10,  1.03648645e-10,  8.30225666e-10,  1.57042823e-09,\n",
       "        1.56147628e-09,  6.85477453e-10,  6.00230976e-12,  2.91725577e-09,\n",
       "        1.84500983e-08,  6.69775062e-08,  1.93903119e-07,  4.62686238e-07,\n",
       "        1.04002318e-06,  1.91174580e-06,  2.38510839e-06,  4.03184561e-06,\n",
       "        6.83488480e-06,  1.82919687e-05,  2.09881954e-05,  2.08803473e-05,\n",
       "        2.21523495e-05,  1.40516140e-05,  6.44777606e-06,  4.90681168e-06,\n",
       "       -1.22348183e-06, -7.85770681e-07, -1.44148689e-05, -1.05966301e-05,\n",
       "       -1.89473831e-05, -3.69965710e-06, -1.12832367e-05, -3.56014370e-05,\n",
       "       -1.35434857e-06, -4.75865454e-06, -3.23347558e-06, -2.36963388e-07,\n",
       "       -2.48328433e-08, -5.80257620e-08, -1.70943167e-07, -3.57315002e-07,\n",
       "       -6.49673893e-07, -1.09386929e-06])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls.solutions.get() - np.array(vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.08 s ± 260 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit ls.solve() # not bad for solving 50 different LASSO problems simultaneously -- and without GPU!\n",
    "# we will get even better relative performance as problem size increases and GPU is implemented"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.004407873999298317"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and just another sanity check: LassoSolver once again matches with CVXPY\n",
    "ls.solve()\n",
    "np.linalg.norm(ls.X[:,-1] - x.value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.18696284294128418\n"
     ]
    }
   ],
   "source": [
    "from time import time\n",
    "tic = time()\n",
    "ls.solve()\n",
    "toc = time()\n",
    "print(toc-tic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.77291905e-01, 4.16801762e-01, 4.71700250e-01, 5.47980911e-01,\n",
       "       6.53971500e-01, 8.01242930e-01, 1.00587202e+00, 1.29019571e+00,\n",
       "       1.68524767e+00, 2.23414256e+00, 2.99677543e+00, 4.05634588e+00,\n",
       "       5.52841255e+00, 7.57345311e+00, 1.04142759e+01, 1.43601346e+01,\n",
       "       1.98400848e+01, 2.74490397e+01, 3.80112007e+01, 5.26671374e+01,\n",
       "       7.29927976e+01, 1.01160649e+02, 1.40158808e+02, 1.94086374e+02,\n",
       "       2.68523963e+02, 3.71008303e+02, 5.11632570e+02, 7.03754831e+02,\n",
       "       9.64684947e+02, 1.31638713e+03, 1.78561417e+03, 2.40261896e+03,\n",
       "       3.19803411e+03, 4.19999079e+03, 5.41723236e+03, 6.83762669e+03,\n",
       "       8.40369929e+03, 9.98345685e+03, 1.14164258e+04, 1.24909583e+04,\n",
       "       1.30425732e+04, 1.31596845e+04, 1.31655210e+04, 1.31655210e+04,\n",
       "       1.31655210e+04, 1.31655210e+04, 1.31655210e+04, 1.31655210e+04,\n",
       "       1.31655210e+04, 1.31655210e+04])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls.solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[600]"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls.num_iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.15071319e-12,  5.00088859e-12,  3.91908728e-13,  2.26664243e-11,\n",
       "        2.70840017e-11,  1.99382733e-11,  1.22346577e-13,  4.10560475e-12,\n",
       "        2.50843790e-11,  6.70574707e-14,  4.28226343e-11,  3.48165941e-13,\n",
       "       -8.88178420e-16,  3.17132987e-11,  3.26849658e-13,  3.95772304e-12,\n",
       "        5.05551156e-11,  4.92768493e-10,  6.61017907e-10,  5.54152280e-10,\n",
       "        5.67564484e-09,  9.83858683e-09,  1.11589316e-08,  1.17243530e-08,\n",
       "        4.67383984e-07,  2.22563244e-07,  9.64381002e-08,  2.27995088e-07,\n",
       "        2.12738087e-07,  2.22895096e-07,  1.61475600e-06,  1.37308598e-06,\n",
       "        2.29492844e-06,  1.02773993e-06,  1.44165124e-05,  1.05966228e-05,\n",
       "        1.89474013e-05,  3.69963163e-06,  1.12829639e-05,  3.54047952e-05,\n",
       "       -2.31481499e-06, -8.07198739e-06, -9.52437586e-06, -1.25208862e-05,\n",
       "       -1.27330186e-05, -1.26998239e-05, -1.25869065e-05, -1.24005328e-05,\n",
       "       -1.21081757e-05, -1.16639821e-05])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vals - ls.solutions.get()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "colab": {
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  "kernelspec": {
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   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
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   "mimetype": "text/x-python",
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