diff --git a/ADMM.ipynb b/ADMM.ipynb new file mode 100644 index 0000000..749287a --- /dev/null +++ b/ADMM.ipynb @@ -0,0 +1,863 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "EE609 ADMM.ipynb", + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "y5LmF6V8j3Jm" + }, + "source": [ + "**Group Members:** Raunak Shah, Varun Goyal, Ishanh Misra \\\\\n", + "**Project Mode:** Mixed \\\\\n", + "**Topic:** ADMM" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "9sDycaX8j3uB" + }, + "source": [ + "import numpy as np\n", + "import scipy\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "np.random.seed(70) #for reproducibility" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "HX2kpp39AVCq" + }, + "source": [ + "### Initializations for QP - ADMM" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "7tkjZva1r1Uv" + }, + "source": [ + "Original Problem: \n", + "\n", + "$min_{u} \\;\\frac{1}{2}u^TQu+q^Tu \\;$ s.t. $Au\\leq b$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XEL7meDQnvOG" + }, + "source": [ + "**IMPORTANT:** \n", + "If you want to run just ADMM to replicate Fig. 1 and 2 of the term paper, set Nu=500 and Nb=250 and run ONLY the ADMM cells (AMA will take too long). \\\\\n", + "If you want to run AMA and compare it with ADMM to replicate Fig. 3 of the term paper, set Nu=50 and Nb=25 and run all the cells." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "ItIAZoI8kdME" + }, + "source": [ + "Nu = 500\n", + "Nb = 250\n", + "tau = 1\n", + "A = np.random.normal(0, 1, (Nb, Nu))" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "2NkgVdue2Xvn" + }, + "source": [ + "Q_temp = np.random.normal(0, 1, (Nu, Nu))\n", + "Q = np.dot(Q_temp.T, Q_temp) # Q is psd" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "Bl0DR9vR41l0" + }, + "source": [ + "q = np.random.normal(0, 1, Nu)\n", + "b = np.random.normal(0, 1, Nb)\n", + "\n", + "v_init = np.random.normal(0, 1, Nb)\n", + "lambd_init = np.random.rand(Nb)" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ucrByN1PASmi" + }, + "source": [ + "### Standard ADMM" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "YYLWykyWpeYe" + }, + "source": [ + "v = v_init\n", + "lambd = lambd_init\n", + "primal_res = []\n", + "dual_res = []\n", + "iters = np.arange(0, 500)\n", + "\n", + "cached_inv = np.linalg.inv((Q + tau*np.matmul(A.T, A)))\n", + "\n", + "for k in iters:\n", + " u = np.matmul(cached_inv, np.dot(A.T, lambd+tau*v) - q) # u-update\n", + " v_prev = v\n", + " v = np.minimum(np.dot(A, u) - (lambd/tau), b) # v-update\n", + " lambd = lambd + tau*(v - np.dot(A, u)) # lambda-update\n", + "\n", + " primal_res.append(np.linalg.norm(v - np.dot(A, u), 2))\n", + " dual_res.append(np.linalg.norm(-tau*np.matmul(A.T, v - v_prev), 2))" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 388 + }, + "id": "GzbAjWJlp-hI", + "outputId": "2db86ed2-ebae-4cc6-f82e-99cad7302f7a" + }, + "source": [ + "plt.figure(figsize=(8,6))\n", + "plt.plot(primal_res, label=\"Primal residual\")\n", + "plt.plot(dual_res, label=\"Dual residual\")\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(\"Iterations\")\n", + "plt.ylabel(\"Residual Error\")\n", + "plt.legend()\n", + "plt.grid()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "UvESj7gNq3aX" + }, + "source": [ + "### FISTA-Accelerated ADMM for Strongly Convex H and G" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "lH8OBlD9itOg" + }, + "source": [ + "Note that here $G(v) = I_{v\\leq b}$ is NOT strongly convex (proved in the term paper), so this algorithm should not converge as per the theory. We still implemented it, and that is what we observed below:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "H3Ydmn9cq2uW" + }, + "source": [ + "v = v_init\n", + "v_hat = v_init\n", + "lambd = lambd_init\n", + "lambd_hat = lambd_init\n", + "alpha = 1\n", + "\n", + "primal_res_acc = []\n", + "dual_res_acc = []\n", + "iters = np.arange(0, 500)\n", + "\n", + "cached_inv = np.linalg.inv((Q + tau*np.matmul(A.T, A)))\n", + "\n", + "for k in iters:\n", + " u = np.matmul(cached_inv, np.dot(A.T, lambd_hat+tau*v_hat) - q)\n", + "\n", + " v_prev = v\n", + " v = np.minimum(np.dot(A, u) - (lambd_hat/tau), b)\n", + "\n", + " lambd_prev = lambd\n", + " lambd = lambd_hat + tau*(v - np.dot(A, u))\n", + "\n", + " alpha_prev = alpha\n", + " alpha = (1+np.sqrt(1+4*(alpha**2)))/2\n", + "\n", + " v_hat = v + (alpha_prev-1)*(v - v_prev)/alpha\n", + " lambd_hat = lambd + (alpha_prev-1)*(lambd-lambd_prev)/alpha\n", + "\n", + " primal_res_acc.append(np.linalg.norm(v - np.dot(A, u), 2))\n", + " dual_res_acc.append(np.linalg.norm(-tau*np.matmul(A.T, v - v_prev), 2))" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 388 + }, + "id": "Vkn2JLyRrTVz", + "outputId": "5f4a5226-7d3e-4952-af3d-aa77dbb67e2c" + }, + "source": [ + "plt.figure(figsize=(8,6))\n", + "plt.plot(iters, primal_res, label=\"Primal residual\")\n", + "plt.plot(iters, dual_res, label=\"Dual residual\")\n", + "plt.plot(iters, primal_res_acc, label=\"Primal residual (acc)\")\n", + "plt.plot(iters, dual_res_acc, label=\"Dual residual (acc)\")\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(\"Iterations\")\n", + "plt.ylabel(\"Residual Error\")\n", + "plt.legend()\n", + "plt.grid()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "utH2gedC9VN9" + }, + "source": [ + "### FISTA-Accelerated ADMM with Restart Method" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "P2Sqh0Xp9XCC" + }, + "source": [ + "v = v_init\n", + "v_hat = v_init\n", + "lambd = lambd_init\n", + "lambd_hat = lambd_init\n", + "alpha = 1\n", + "c = 0\n", + "\n", + "primal_res_accr = []\n", + "dual_res_accr = []\n", + "iters = np.arange(0, 500)\n", + "\n", + "cached_inv = np.linalg.inv((Q + tau*np.matmul(A.T, A)))\n", + "\n", + "eta = 0.999\n", + "for k in iters:\n", + " u = np.matmul(cached_inv, np.dot(A.T, lambd_hat+tau*v_hat) - q)\n", + "\n", + " v_prev = v\n", + " v = np.minimum(np.dot(A, u) - (lambd_hat/tau), b)\n", + "\n", + " lambd_prev = lambd\n", + " lambd = lambd_hat + tau*(v - np.dot(A, u))\n", + "\n", + " c_prev = c\n", + " c = (np.linalg.norm(lambd - lambd_hat, 2)**2)/tau + tau*(np.linalg.norm(v - v_hat, 2)**2)\n", + " \n", + " alpha_prev = alpha\n", + " if c < eta*c_prev:\n", + " alpha = (1+np.sqrt(1+4*(alpha**2)))/2\n", + "\n", + " v_hat = v + (alpha_prev-1)*(v - v_prev)/alpha\n", + " lambd_hat = lambd + (alpha_prev-1)*(lambd-lambd_prev)/alpha \n", + " else:\n", + " alpha = 1\n", + " v_hat = v_prev\n", + " lambd_hat = lambd_prev\n", + " c = c/eta\n", + "\n", + " primal_res_accr.append(np.linalg.norm(v - np.dot(A, u), 2))\n", + " dual_residual = np.linalg.norm(-tau*np.matmul(A.T, v - v_prev), 2)\n", + " if dual_residual == 0:\n", + " dual_res_accr.append(dual_res_accr[-1])\n", + " else:\n", + " dual_res_accr.append(dual_residual)\n", + "\n", + "lambd_opt = lambd # This is the final optimal lambda. We use this to help track the error for AMA below." + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 388 + }, + "id": "NAvBHc1qHFf5", + "outputId": "6ad02302-9da1-41d2-8b54-5734fb99057a" + }, + "source": [ + "plt.figure(figsize=(8,6))\n", + "plt.plot(iters, primal_res, label=\"Primal residual\")\n", + "plt.plot(iters, dual_res, label=\"Dual residual\")\n", + "plt.plot(iters, primal_res_accr, label=\"Primal residual (restart)\")\n", + "plt.plot(iters, dual_res_accr, label=\"Dual residual (restart)\")\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(\"Iterations\")\n", + "plt.ylabel(\"Residual Error\")\n", + "plt.legend()\n", + "plt.grid()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "APEjCD9bNkVB" + }, + "source": [ + "Note that in the ADMM experiments above, convergence is faster when Nu=50 and Nb=25 compared to Nu=500 and Nb=250. This is expected since the dimensionality of the problem is smaller in the first case. The effectiveness of the restart method is more clearly observed in the problem with higher dimensionality." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "HZIoN7yIobqB" + }, + "source": [ + "### Sensitivity of convergence of ADMM to the value of $\\tau$\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "WDFSGq0loR24" + }, + "source": [ + "# Normal ADMM\n", + "tau = 1\n", + "taus = []\n", + "tau_sens = []\n", + "for tau in np.logspace(-2, 2, 26):\n", + " v = v_init\n", + " lambd = lambd_init\n", + " iters = np.arange(0, 10000)\n", + " cached_inv = np.linalg.inv((Q + tau*np.matmul(A.T, A)))\n", + "\n", + " for k in iters:\n", + " u = np.matmul(cached_inv, np.dot(A.T, lambd+tau*v) - q)\n", + " v_prev = v\n", + " v = np.minimum(np.dot(A, u) - (lambd/tau), b)\n", + " lambd = lambd + tau*(v - np.dot(A, u))\n", + "\n", + " primal_residual = np.linalg.norm(v - np.dot(A, u), 2)\n", + " dual_residual = np.linalg.norm(-tau*np.matmul(A.T, v - v_prev), 2)\n", + "\n", + " if primal_residual < 10**(-5) and dual_residual < 10**(-5):\n", + " taus.append(tau)\n", + " tau_sens.append(k)\n", + " break" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "o9nrbMx0oSIT" + }, + "source": [ + "# Accelerated ADMM + Restart Method\n", + "tau = 1\n", + "taus_acc = []\n", + "tau_sens_acc = []\n", + "for tau in np.logspace(-2, 2, 26):\n", + " v = v_init\n", + " v_hat = v_init\n", + " lambd = lambd_init\n", + " lambd_hat = lambd_init\n", + " alpha = 1\n", + "\n", + " iters = np.arange(0, 10000)\n", + " cached_inv = np.linalg.inv((Q + tau*np.matmul(A.T, A)))\n", + "\n", + " eta = 0.999\n", + " for k in iters:\n", + " u = np.matmul(cached_inv, np.dot(A.T, lambd_hat+tau*v_hat) - q)\n", + "\n", + " v_prev = v\n", + " v = np.minimum(np.dot(A, u) - (lambd_hat/tau), b)\n", + "\n", + " lambd_prev = lambd\n", + " lambd = lambd_hat + tau*(v - np.dot(A, u))\n", + "\n", + " c_prev = c\n", + " c = (np.linalg.norm(lambd - lambd_hat, 2)**2)/tau + tau*(np.linalg.norm(v - v_hat, 2)**2)\n", + " \n", + " alpha_prev = alpha\n", + " if c < eta*c_prev:\n", + " alpha = (1+np.sqrt(1+4*(alpha**2)))/2\n", + "\n", + " v_hat = v + (alpha_prev-1)*(v - v_prev)/alpha\n", + " lambd_hat = lambd + (alpha_prev-1)*(lambd-lambd_prev)/alpha \n", + " else:\n", + " alpha = 1\n", + " v_hat = v_prev\n", + " lambd_hat = lambd_prev\n", + " c = c/eta\n", + "\n", + " primal_residual = np.linalg.norm(v - np.dot(A, u), 2)\n", + " dual_residual = np.linalg.norm(-tau*np.matmul(A.T, v - v_prev), 2)\n", + "\n", + " if primal_residual < 10**(-5) and dual_residual < 10**(-5):\n", + " taus_acc.append(tau)\n", + " tau_sens_acc.append(k)\n", + " break" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 302 + }, + "id": "Ai5VwqSzoe-L", + "outputId": "0421e5d8-da43-4cdb-c433-4c411848078e" + }, + "source": [ + "plt.plot(taus, tau_sens, 'o-', label='Normal ADMM')\n", + "plt.plot(taus_acc, tau_sens_acc, 'o-', label='Accelerated ADMM + Restart')\n", + "plt.xscale(\"log\")\n", + "plt.grid()\n", + "plt.ylabel(\"Iterations for Convergence\")\n", + "plt.xlabel(\"tau\")\n", + "plt.legend()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 71 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "9ChUtbCuCYpy" + }, + "source": [ + "### Normal AMA" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "NP5xUxj_pT9S" + }, + "source": [ + "**IMPORTANT**: If you want to run AMA, set Nu=50 and Nb=25 above and run all the cells again" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "rUNKugY97Bce" + }, + "source": [ + "def dual_objective(lamb):\n", + " \"\"\"Computes the dual objective D(lambda)\"\"\"\n", + " temp = np.dot(A.T, lamb)-q\n", + " return -0.5*np.matmul(temp.T, np.matmul(np.linalg.inv(Q), temp))+np.dot(b, lamb)" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "1Op0CBBVCaU0" + }, + "source": [ + "v = v_init\n", + "lambd = lambd_init\n", + "ama_primal_res = []\n", + "ama_dual_res = []\n", + "\n", + "iters = np.arange(0, 5000)\n", + "tau = np.min(np.linalg.eigvalsh(Q))/np.max(np.abs(np.linalg.eigvalsh(np.matmul(A.T, A))))\n", + "\n", + "cached_inv = np.linalg.inv(Q)\n", + "for k in iters:\n", + " u = np.matmul(cached_inv, np.dot(A.T, lambd) - q)\n", + "\n", + " v_prev = v\n", + " v = np.minimum(np.dot(A, u) - (lambd/tau), b)\n", + "\n", + " lambd_prev = lambd\n", + " lambd = lambd + tau*(v - np.dot(A, u))\n", + " \n", + " ama_primal_res.append(np.linalg.norm(v - np.dot(A, u), 2))\n", + " ama_dual_res.append(dual_objective(lambd_opt) - dual_objective(lambd))" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "eSz-ZuRLK9fm" + }, + "source": [ + "### Fast AMA for strongly convex H and convex G" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "LaeMFt7DK8_W" + }, + "source": [ + "v = v_init\n", + "v_hat = v_init\n", + "lambd = lambd_init\n", + "lambd_hat = lambd_init\n", + "alpha = 1\n", + "fast_ama_primal_res = []\n", + "fast_ama_dual_res = []\n", + "\n", + "iters = np.arange(0, 5000)\n", + "\n", + "cached_inv = np.linalg.inv(Q)\n", + "for k in iters:\n", + " u = np.matmul(cached_inv, np.dot(A.T, lambd_hat) - q)\n", + "\n", + " v_prev = v\n", + " v = np.minimum(np.dot(A, u) - (lambd_hat/tau), b)\n", + "\n", + " lambd_prev = lambd\n", + " lambd = lambd_hat + tau*(v - np.dot(A, u))\n", + "\n", + " alpha_prev = alpha\n", + " alpha = (1+np.sqrt(1+4*(alpha**2)))/2\n", + "\n", + " lambd_hat = lambd + (alpha_prev-1)*(lambd-lambd_prev)/alpha \n", + "\n", + " fast_ama_primal_res.append(np.linalg.norm(v - np.dot(A, u), 2))\n", + " fast_ama_dual_res.append(dual_objective(lambd_opt) - dual_objective(lambd))" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "2hunnfA7nBt_" + }, + "source": [ + "### AMA with Restart" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "N_sHWuPsnDf9" + }, + "source": [ + "v = v_init\n", + "v_hat = v_init\n", + "lambd = lambd_init\n", + "lambd_hat = lambd_init\n", + "alpha = 1\n", + "\n", + "ama_primal_res_accr = []\n", + "ama_dual_res_accr = []\n", + "iters = np.arange(0, 5000)\n", + "\n", + "cached_inv = np.linalg.inv(Q)\n", + "\n", + "for k in iters:\n", + " u = np.matmul(cached_inv, np.dot(A.T, lambd_hat) - q)\n", + "\n", + " v_prev = v\n", + " v = np.minimum(np.dot(A, u) - (lambd_hat/tau), b)\n", + "\n", + " lambd_prev = lambd\n", + " lambd = lambd_hat + tau*(v - np.dot(A, u))\n", + " \n", + " alpha_prev = alpha\n", + " if dual_objective(lambd) >= dual_objective(lambd_prev):\n", + " alpha = (1+np.sqrt(1+4*(alpha**2)))/2\n", + " lambd_hat = lambd + (alpha_prev-1)*(lambd-lambd_prev)/alpha\n", + " else:\n", + " alpha = 1\n", + " lambd_hat = lambd_prev\n", + "\n", + " ama_primal_res_accr.append(np.linalg.norm(v - np.dot(A, u), 2))\n", + " ama_dual_res_accr.append(dual_objective(lambd_opt) - dual_objective(lambd))" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "FD_eq77RkQfc" + }, + "source": [ + "### Comparison with Normal ADMM" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "rLKo20ROkQoe" + }, + "source": [ + "v = v_init\n", + "lambd = lambd_init\n", + "admm_primal_res = []\n", + "admm_dual_res = []\n", + "tau = 1\n", + "iters = np.arange(0, 5000)\n", + "\n", + "cached_inv = np.linalg.inv((Q + tau*np.matmul(A.T, A)))\n", + "\n", + "for k in iters:\n", + " u = np.matmul(cached_inv, np.dot(A.T, lambd+tau*v) - q)\n", + " v_prev = v\n", + " v = np.minimum(np.dot(A, u) - (lambd/tau), b)\n", + " lambd = lambd + tau*(v - np.dot(A, u))\n", + "\n", + " admm_primal_res.append(np.linalg.norm(v - np.dot(A, u), 2))\n", + " admm_dual_res.append(abs(dual_objective(lambd_opt) - dual_objective(lambd)))" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "UHCbnqJVt1VY" + }, + "source": [ + "### AMA: Plots" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 503 + }, + "id": "5QyDXnXpLpTu", + "outputId": "bf182d5c-ec12-426f-c6d4-c2bf7ae1e7ad" + }, + "source": [ + "plt.figure(figsize=(8,8))\n", + "plt.subplot(211)\n", + "plt.plot(iters, ama_primal_res, label=\"AMA primal residuals\")\n", + "plt.plot(iters, fast_ama_primal_res, label=\"Fast AMA primal residuals\")\n", + "plt.plot(iters, ama_primal_res_accr, label=\"Restart AMA primal residuals\")\n", + "\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(\"Iterations\")\n", + "plt.ylabel(\"Primal Residual Error\")\n", + "plt.legend()\n", + "plt.grid()\n", + "\n", + "plt.subplot(212)\n", + "plt.plot(iters, ama_dual_res, label=\"AMA dual error\")\n", + "plt.plot(iters, fast_ama_dual_res, label=\"Fast AMA dual error\")\n", + "plt.plot(iters, ama_dual_res_accr, label=\"Restart AMA dual error\")\n", + "\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(\"Iterations\")\n", + "plt.ylabel(\"Dual Objective Error\")\n", + "plt.legend()\n", + "plt.grid()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "ENE_R_ZukxLj", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 497 + }, + "outputId": "9238ef37-e9e9-47be-bd5b-dd399db7336a" + }, + "source": [ + "# This plot shows how normal ADMM performs in comparison to the AMA variants. \n", + "plt.figure(figsize=(8,8))\n", + "plt.subplot(211)\n", + "plt.plot(iters, admm_primal_res, label=\"Normal ADMM primal residuals\") \n", + "plt.plot(iters, ama_primal_res, label=\"AMA primal residuals\")\n", + "plt.plot(iters, fast_ama_primal_res, label=\"Fast AMA primal residuals\")\n", + "plt.plot(iters, ama_primal_res_accr, label=\"Restart AMA primal residuals\")\n", + "\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(\"Iterations\")\n", + "plt.ylabel(\"Primal Residual Error\")\n", + "plt.legend()\n", + "plt.grid()\n", + "\n", + "plt.subplot(212)\n", + "plt.plot(iters, admm_dual_res, label=\"Normal ADMM dual error\")\n", + "plt.plot(iters, ama_dual_res, label=\"AMA dual error\")\n", + "plt.plot(iters, fast_ama_dual_res, label=\"Fast AMA dual error\")\n", + "plt.plot(iters, ama_dual_res_accr, label=\"Restart AMA dual error\")\n", + "\n", + "plt.yscale(\"log\")\n", + "plt.xlabel(\"Iterations\")\n", + "plt.ylabel(\"Dual Objective Error\")\n", + "plt.legend()\n", + "plt.grid()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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