{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 1. Introduction\n", "First load the necessary packages for this training course" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.1 Vector Norms\n", "Recall the following vector norms:\n", "\n", "$\n", "\\begin{align}\n", "&\\lVert x \\rVert_1 = \\sum_i \\lvert x_i \\rvert \\\\\n", "&\\lVert x \\rVert_2 = \\sqrt{\\sum_i x_i^2} \\\\\n", "&\\lVert x \\rVert_\\infty = \\max_i \\lvert x_i \\rvert\n", "\\end{align}\n", "$\n", "\n", "**Coding Task:**\n", "\n", "For each of the above norms, find and plot the boundaries of the regions in 2D where $\\lVert x \\rVert \\le 1$ for $x=(x_1,x_2)$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAD4CAYAAADhNOGaAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAwlElEQVR4nO3deXxU9b3/8dcnO5CdJEA2CATZlSUGBK2iqLgBLlXAtqioba313i63tT/b2uty6723rda6VAS3uqBVq1TxugCKiCBh3yGEQBJC9n3PzPf3xxxoxIQkzCQnM/N5Ph7zmDNnmXmfBOaT8/2e8z1ijEEppZT/CrA7gFJKKXtpIVBKKT+nhUAppfycFgKllPJzWgiUUsrPBdkd4EzExcWZYcOG2R1DKaW8yubNm0uNMfGnzvfKQjBs2DCysrLsjqGUUl5FRI60N1+bhpRSys9pIVBKKT+nhUAppfycFgKllPJzWgiUUsrPeaQQiMhzIlIsIrs6WC4i8riIZIvIDhGZ3GbZIhE5aD0WeSKPUkqprvPUEcELwOzTLL8CGGk97gSeBhCRWOB+YCqQCdwvIjEeyqSUUqoLPHIdgTFmrYgMO80qc4GXjGvM6w0iEi0iQ4CLgI+NMeUAIvIxroLymidyKeUJxhjK65qpa3LQ1OqgqdVJY4vruanVQVOLs915BogLDyUhIpSEyFDiI0KJCw8lOFBbZFXf0lsXlCUBeW1e51vzOpr/DSJyJ66jCVJTU3smpfJrTqfhWFUD2cW1Jx8HreeqhhaPfIYIxPYPIT7CVRgSIsJIiHQVi/iIUNITwjkrIYKAAPHI5ynVFV5zZbExZgmwBCAjI0PvpqPOmMNpOFJWd/JLvu2jocVxcr2BA0IYkRDO1WcPYXh8OFH9ggkNCiA0KICw4EDX9InnduYZA6W1TRTXNFFc3UhJbRPF1a7XJTVNlNQ0kl1cS0lNE63Of/2TjggLYlJqDBlDY5gyNIaJKdEMCPWa/6rKC/XWv64CIKXN62RrXgGu5qG28z/tpUzKj1Q3trD2QAmr9xazZn8xFfX/+gt/SFQY6QnhzM9MYWRCBOkJ4aQnhBM7IMTtz02M7kdidL/TruN0GiobWiiqbmRvYTVZRyrYcqSCRz85gDEQIDBmSCRTrMIwZWgMSdH9ENGjBuUZ4qlbVVp9BO8ZY8a3s+wq4G7gSlwdw48bYzKtzuLNwImziLYAU070GXQkIyPD6FhDqjM5JbWs3lfMqr3FbMotp9VpiO4fzMxRCZw3YiCjBkUwIiGc8D7613ZVQwvb8irZnFvO5qMVbD1aSX2z64hlcGQYU4bGMG14LFdOGMLA8FCb0ypvICKbjTEZ35jviUIgIq/h+ss+DijCdSZQMIAx5q/i+tPlCVwdwfXArcaYLGvb24D/Z73Vw8aY5zv7PC0Eqj3NrU6ycstZta+Y1fuKOVxaB8CoQRFcPCaBS0YnMCk1hkAvbX9vdTjZd7yGLUcr2HykgqzcCgoqGwgKEC4aFc91k5O5eHQCYcGBdkdVfVSPFoLepoVAndDqcPLh7iJW7ixk7YESappaCQkM4LwRA7lkTAIzRyWQEtvf7pg95kBRDW9tyeedrQUUVTcRGRbENeckct3kZCanRmvzkfoaLQTKp1Q1tPD6pqO88EUux6oaiY8I5ZLRCVw8OoEZ6XF+17nqcBrWHyrlrc35/N/u4zS2OBk2sD/XTU7m2klJPl0MVddpIVA+4UhZHc9/kcvfs/Koa3YwNS2W2y8YzsWjE7y2ycfTapta+WBnIW9vKeDLnDIApqbFcv3kZK6YMJiIsGCbEyq7aCFQXssYw6bcCpaty+GjPUUEijDnnERuOz+N8UlRdsfr0/Ir6nlnawFvbykgp7SOiNAg7vjWcG47P63PdpKrnqOFQHmdFoeTlTsLWfr5YXYWVBHdP5ibp6byvfOGMSgyzO54XsUYw9a8Sv766SE+2lNE7IAQ7rpoBN+ZNlQ7l/2IFgLlNeqaWnnpyyO8uD6X49WNDI8fwOLz07huUjL9QvRLy13b8ir540f7+fxgKYMjw/jxJencmJGiQ1/4AS0Eqs8zxrBy53EefG8Px6sbOT89jsXnp3HhWfE65EIP+PJQGX/4aD+bj1SQGtufn1w6kjnnJGlfiw/TQqD6tJySWu5fsZvPD5YydkgkD84bz5ShOhBtTzPGsGZ/MX/48AB7Cqs5a1A4P710FJePG6SnnvogLQSqT2podvDUp9k881kOoUEB/Oyys/jOtKEEaTNFr3I6DSt3FfKnjw6QU1rH2clR/Mflo7hgZLzd0ZQHaSFQfc4ne4r43T93k1/RwLWTkvjVlaNJiNBOYDu1Opy8vbWAP39ykILKBm6Yksz914zVU059REeFQM8fU70ur7ye//znHj7ZW8TIhHBeu2Ma540YaHcsBQQFBnBjRgpzJybyxOpsnlyTzYacMv5040Qy02Ltjqd6iB4RqF7T1Org2bU5PLEmmwAR/u2Skdx2fpqerdKHbT5SwU/f2MbR8np+cOEIfjLrLEKC9PflrfSIQNlq97EqfvzqVnJK67hywmB+c/VYhkSdfnhmZb8pQ2NYec8FPPjeHp7+9BCf7S/hsfkTOWtQhN3RlAdpaVc97t1tBVz/9HoaWhy8eFsmT908RYuAFxkQGsQj15/Nku9Ooai6kav/so5l6w7jdHpfa4Jqnx4RqB7T6nDy+w/2sWzdYTLTYnnq5snE6bj5XuuycYOZlBrDvW/t4MH39rB6XxF/+PY5WtR9gB4RqB5RVtvEd5d9xbJ1h7ll+jBeuX2qFgEfEB8RytJFGfzXtRPYcqSSyx9dy4rtx+yOpdykhUB53K6CKuY88QVbjlbwx2+fw+/mjNMOYR8iIiycmsoH/3YBw+PDuee1rfz6nZ04tKnIa3nkf6eIzBaR/SKSLSL3trP8URHZZj0OiEhlm2WONstWeCKPss9bm/O5/un1ALz5g+lcPyXZ5kSqpwyLG8CbPziPO781nJc3HOVHr2yhscVhdyx1BtzuIxCRQOBJ4FIgH9gkIiuMMXtOrGOM+Umb9X8MTGrzFg3GmInu5lD2anE4efj9vbywPpdpw2N5cuFkvY+uHwgKDOD/XTmGhIhQHnp/L7c8/xVLvpdBpF6A5lU8cUSQCWQbY3KMMc3AcmDuadZfALzmgc9VfURJTRM3L93IC+tzWXx+Gi8vnqpFwM/cfsFwHrtpIlm5Fdz0zAaKqxvtjqS6wROFIAnIa/M635r3DSIyFEgDVreZHSYiWSKyQUTmdfQhInKntV5WSUmJB2IrTzhcWsecJ9axPa+Sx26ayG+uHqvjBPmpeZOSWHbLuRwpq+P6v64nt7TO7kiqi3r7f+x84E1jTNuGxKHWlW4LgcdEZER7GxpjlhhjMowxGfHxOhBWX5BXXs/CZzfQ1OrkrR9OZ96kduu/8iMXnhXPq3dMo7axleufXs/O/Cq7I6ku8EQhKABS2rxOtua1Zz6nNAsZYwqs5xzgU77ef6D6qGOVDSxcuoH6ZgcvL56qt4xUJ01MiebNH04nLDiQ+Uu+ZN3BUrsjqU54ohBsAkaKSJqIhOD6sv/G2T8iMhqIAb5sMy9GREKt6ThgBrDn1G1V31Jc3cjNSzdSWdfCS7dlMjYx0u5Iqo8ZER/OWz+cTnJMf2594Sve26HXGvRlbhcCY0wrcDfwIbAXeMMYs1tEHhCROW1WnQ8sN18f5W4MkCUi24E1wCNtzzZSfU9pbRMLl26kqLqRF247l3NSou2OpPqowVFhvPH985iYEs2PX9vK377MtTuS6oCOPqq6rLK+mflLNpBbVscLt2YybbgOHa0619ji4O5Xt/DJ3mKeXDiZq84eYnckv9XR6KN6eofqkurGFr677CtySut49nsZWgRUl4UFB/LEwslMGRrDT9/YxtajFXZHUqfQQqA6VdvUyi3PfcW+49U8ffNkvX2h6raw4ECWfHcKCZGh3PFSFnnl9XZHUm1oIVCn1dDsYPELm9ieX8VfFkzikjGD7I6kvNTA8FCev+VcmlqdLH5xE9WNLXZHUhYtBKpDDqfhBy9vZlNuOY/eNJHZ47VtV7knPSGCv35nCjklddz96lZaHU67Iym0EKjTeHzVQT47UMJD8yYw55xEu+MoHzEjPY4H541n7YESfvfP3XjjCSu+Rm9Mo9q1PruUx1cf5PrJySycmmp3HOVjFmSmkltaxzNrcxgeF85t56fZHcmvaSFQ31Bc08g9y7cxIj6cB+eNszuO8lG/nD2aw6V1PPj+HlJj+zNrrPY/2UWbhtTXOJyGn7y+jdqmFp5cOJn+Ifq3guoZAQHCY/MnMj4xinuWb2X3MR2XyC5aCNTXPLkmmy+yy/jPOeMYNTjC7jjKx/UPCWLpogyi+gWz+IUsKuqa7Y7kl7QQqJM25JTx2CcHmDcxkRszUjrfQCkPGBQZxrPfy6C0tokH39MRZuyghUABrjGE7nltK8MGDuChaycgInZHUn5kfFIUd100gre3FrBmX7HdcfyOFgKF0+oXqGxo4YmFkwkP1X4B1ft+dHE6IxPCue8fO6nRi816lRYCxdOfHeLzg6Xcf81YHVJa2SY0KJD/ueFsCqsb+e//22d3HL+ihcDPZeWW88eP9nP12UNYmKnXCyh7TUqN4bYZaby84SgbcsrsjuM3tBD4MYfT8Ot3djEkqh+/v077BVTf8LPLziI1tj/3vrWDhmZH5xsot3mkEIjIbBHZLyLZInJvO8tvEZESEdlmPW5vs2yRiBy0Hos8kUd1zZub89h3vIZ7rxhNRFiw3XGUAlynlD5y3QRyy+p57JMDdsfxC24XAhEJBJ4ErgDGAgtEZGw7q75ujJloPZZa28YC9wNTgUzgfhGJcTeT6lxtUyt/+OgAk1OjuVpvFKL6mOnpcSzITOHZz3PYnldpdxyf54kjgkwg2xiTY4xpBpYDc7u47eXAx8aYcmNMBfAxMNsDmVQnnvnsECU1Tfz66rHaJKT6pF9dOYb4iFB++dYOmlt1lNKe5IlCkATktXmdb8071fUiskNE3hSRE1crdXVb5UHHKhtYsjaHOeckMjlVD8BU3xQZFszD8yaw73gNT396yO44Pq23Oov/CQwzxpyN66/+F7v7BiJyp4hkiUhWSUmJxwP6k//5v30Y4BezR9kdRanTmjV2EHPOSeSJNQcpqGywO47P8kQhKADajkeQbM07yRhTZoxpsl4uBaZ0dds277HEGJNhjMmIj9dbJZ6pbXmVvLPtGLefn0ZyTH+74yjVqV9eMRpj4Nm1OXZH8VmeKASbgJEikiYiIcB8YEXbFUSkbW/kHGCvNf0hcJmIxFidxJdZ81QPMMbw0Ht7iAsP4a6Z6XbHUapLkqL7cd3kJF776iglNU2db6C6ze1CYIxpBe7G9QW+F3jDGLNbRB4QkTnWaveIyG4R2Q7cA9xibVsOPIirmGwCHrDmqR7wwa7jZB2p4GeXjdJhJJRX+eFF6bQ4nCxdp0cFPUG88TZxGRkZJisry+4YXqWp1cGsP33GgJAg3r/nAgID9Ewh5V1+/NpWVu8t4ot7Lya6f4jdcbySiGw2xmScOl+vLPYTL67PJa+8gfuuGqNFQHmlH80cQV2zg+e/yLU7is/RQuAHWhxOln5+mAtGxnHBSO1oV95p9OBILh07iBfW5+ropB6mhcAPrNpbRHFNE4vOG2Z3FKXccvfMdKoaWnh5w1G7o/gULQR+4JWNR0mMCmPm6AS7oyjllnNSorlgZBzL1uXQ2KID0nmKFgIfd6Ssjs8PlnLTuanaN6B8wt0z0ymtbWb5V3pU4ClaCHzcq18dJTBAuOlcvQex8g1Thw/k3GExPLM2R8cg8hAtBD6sqdXB37PyuWR0AoOjwuyOo5TH/GhmOoVVjbyztd2BCFQ3aSHwYR/uLqK8rpmbpw21O4pSHnXhWfGMiB/AW1vy7Y7iE7QQ+LBXNhwhJbYfF6TH2R1FKY8SEa46O5Gvcssprmm0O47X00Lgo7KLa9h4uJwFmakEaCex8kFXTRiCMfDhruN2R/F6Wgh81Ksb8wgOFL49RTuJlW86a1A4I+IH8P7OQrujeD0tBD6oscXBm5vzuHzcYOIjQu2Oo1SPEBGumjCErw6X66ikbtJC4INW7iykurGVhVNT7Y6iVI+68uwhOA38325tHnKHFgIftGpfMQkRoZw3fKDdUZTqUaMGRTA8fgArd2jzkDu0EPgYp9Pw5aEyZqTH6U3plc870Ty08XAZpbXaPHSmtBD4mH3Hayiva2aGnjKq/MSVE6zmIT176Ix5pBCIyGwR2S8i2SJybzvLfyoie0Rkh4isEpGhbZY5RGSb9Vhx6raqe9YfKgVgRro2Cyn/MHpwBMPjBrBSzx46Y24XAhEJBJ4ErgDGAgtEZOwpq20FMowxZwNvAv/TZlmDMWai9ZiDcssX2aUMjxvAkKh+dkdRqleICFdOGMKGHG0eOlOeOCLIBLKNMTnGmGZgOTC37QrGmDXGmHrr5QYg2QOfq07R4nDy1eFypuvRgPIzV1lnD320u8juKF7JE4UgCchr8zrfmteRxcAHbV6HiUiWiGwQkXkdbSQid1rrZZWUlLgV2Fdtz6ukrtnBjBHaP6D8y+jBEQyKDGVTbrndUbxSUG9+mIh8B8gALmwze6gxpkBEhgOrRWSnMebQqdsaY5YAS8B18/peCexlvsguQwTOG6FHBMq/iAgTkqLYVVBldxSv5IkjggKg7TgGyda8rxGRWcB9wBxjzMmGPGNMgfWcA3wKTPJAJr/0xaFSxiVGEt0/xO4oSvW6cYlRHCqppaFZ71zWXZ4oBJuAkSKSJiIhwHzga2f/iMgk4BlcRaC4zfwYEQm1puOAGcAeD2TyO/XNrWw9WqGnjSq/NS4xEqeBvcer7Y7iddwuBMaYVuBu4ENgL/CGMWa3iDwgIifOAvpfIBz4+ymniY4BskRkO7AGeMQYo4XgDGzKraDFYbR/QPmt8UlRAOzW5qFu80gfgTFmJbDylHm/bTM9q4Pt1gMTPJHB363PLiUkMIBzh8XaHUUpWwyJCiN2QAi7CvSIoLv0ymIfsSO/irGJkfQLCbQ7ilK2EBHGJUay65geEXSXFgIfkVdRz9CB/e2OoZStxidFcaCohqZW7TDuDi0EPqDV4aSwqpGUGC0Eyr+NT4yixWE4WFRrdxSvooXABxRWNeJwGlJidVgJ5d/GJUYCsFubh7pFC4EPyCt3jd6hRwTK36XG9iciNEg7jLtJC4EPyKuwCkGsFgLl3wIChLHaYdxtWgh8QF55A4EBwpCoMLujKGW7MUMitY+gm7QQ+IC8inqGRIURFKi/TqViB4RQ29RKi8NpdxSvod8cPiCvvF77B5SyRPULBqC6ocXmJN5DC4EPyKto0DOGlLJE9nMNmFDd2GpzEu+hhcDLNbY4KKlp0iMCpSyRYa4jgio9IugyLQReLl/PGFLqa7RpqPu0EHi5/IoGAJJjtGlIKYDIfnpE0F1aCLxcU6vrzAgdbE4pl5NHBI1aCLpKC4FSyqdoH0H3aSFQSvmUsOAAggOF6gY9a6irPFIIRGS2iOwXkWwRubed5aEi8rq1fKOIDGuz7FfW/P0icrkn8iil/JeIENUvWI8IusHtQiAigcCTwBXAWGCBiIw9ZbXFQIUxJh14FPhva9uxuO5xPA6YDTxlvZ9SSp2xyLBg7SPoBk8cEWQC2caYHGNMM7AcmHvKOnOBF63pN4FLRESs+cuNMU3GmMNAtvV+Sil1xnJK63h/R6HdMbyGJwpBEpDX5nW+Na/ddayb3VcBA7u4LQAicqeIZIlIVklJiQdiK6WUAi/qLDbGLDHGZBhjMuLj4+2Oo5Tqw9ITwrli/GC7Y3gNTxSCAiClzetka16764hIEBAFlHVxW6WU6pbqhpaT1xOoznmiEGwCRopImoiE4Or8XXHKOiuARdb0DcBqY4yx5s+3zipKA0YCX3kgk1LKj1U1tJy8wlh1LsjdNzDGtIrI3cCHQCDwnDFmt4g8AGQZY1YAy4C/iUg2UI6rWGCt9wawB2gFfmSMcbibSSnlvxpbHDS1OvWIoBvcLgQAxpiVwMpT5v22zXQj8O0Otn0YeNgTOZRS6sRpo5FhHvl68wte01ms2hcUIAA0t+rdmJQCTl5RrE1DXaeFwMslRrtGHT1W2WhzEqX6hhNXFGsh6DotBF7uxH0I8qz7Eijl7040DWkfQddpIfBy4aFBxPQPJq9cC4FS8K8b0pwYhVR1TguBD0iJ7c9RLQRKAf8qBHpE0HVaCHxASkz/k3cqU8rfnbhp/Ymb2KvOaSHwAcmx/SioaMDpNHZHUcp2FXXNhAUHEBqkAxl3lRYCH5AS059mh5OiGj1zSKkDxbUMjwu3O4ZX0ULgA06eOVSuzUPKvxlj2F1QxfikSLujeBUtBD4gJcZ1LYGeOaT83fHqRsrqmhmfFGV3FK+ihcAHJMX0Q0SvJVBqd0E1AOMStRB0hxYCHxAaFMigiDBtGlJ+b9exKkRgzJAIu6N4FS0EPiIltp82DSm/t6ugmhHx4fQP0VNHu0MLgY8YMySS3ceqaHHo4HPKf+0+VsX4RO0o7i4tBD5i+oiB1DU72J5XaXcUpWxRWttEYVWjdhSfAS0EPmLa8IGIwLrsUrujKGWL3ce0o/hMuVUIRCRWRD4WkYPWc0w760wUkS9FZLeI7BCRm9ose0FEDovINusx0Z08/iy6fwjjE6NYn11mdxSlbLH7WBUAY7VpqNvcPSK4F1hljBkJrLJen6oe+J4xZhwwG3hMRKLbLP8PY8xE67HNzTx+bXr6QLbmVVDf3Gp3FKV63e6CalJj++tgc2fA3UIwF3jRmn4RmHfqCsaYA8aYg9b0MaAYiHfzc1U7ZoyIo8Vh+Opwud1RlOp1u47pFcVnyt1CMMgYU2hNHwcGnW5lEckEQoBDbWY/bDUZPSoioafZ9k4RyRKRrJKSEjdj+6Zzh8USEhjA+kPaPKT8y9Gyeo6U1TM59Rut06oLOi0EIvKJiOxq5zG37XrGGAN0OPyliAwB/gbcaow5cY7jr4DRwLlALPDLjrY3xiwxxmQYYzLi4/WAoj39QgKZlBrNF9phrPzMyl2uv0cvHzfY5iTeqdOrLowxszpaJiJFIjLEGFNofdEXd7BeJPA+cJ8xZkOb9z5xNNEkIs8DP+9WevUN56fH8cePD1Be10zsgBC74yjVK1buLOSc5KiTAzCq7nG3aWgFsMiaXgS8e+oKIhIC/AN4yRjz5inLhljPgqt/YZebefze9PQ4AL7U5iHlJ/LK69mRX8WVE4bYHcVruVsIHgEuFZGDwCzrNSKSISJLrXVuBL4F3NLOaaKviMhOYCcQBzzkZh6/d05yFOGhQXxxSJuHlH9YudPVsKCF4My5NSCHMaYMuKSd+VnA7db0y8DLHWx/sTufr74pKDCAqWmxrNd+AuUnVu4s5GxtFnKLXlnsgy4cFU9uWT27CqrsjqJUj8orr2d7fhVXjNejAXdoIfBBc89JIjQogFe/Omp3FKV61AfW2UJXabOQW7QQ+KCo/sFcfXYi724toLZJrzJWvuv9nccZnxRJ6kBtFnKHFgIfdfO0VOqaHby7rcDuKEr1iPyKerbnVWonsQdoIfBRk1KiGT04glc2HMV1rZ9SvuWDnccBbRbyBC0EPkpEuHnaUPYUVrM9XzuNle95f2ch4xIjGTpwgN1RvJ4WAh82b2Ii/UMCeWXDEbujKOVR2/Mq2ZZXydyJiXZH8QlaCHxYRFgwcycm8s8dx6hqaLE7jlIe8+SabCLDgliQmWp3FJ+ghcDHLcwcSmOLk39sybc7ilIese94NR/tKeKWGWlEhOm9BzxBC4GPm5AcxTnJUbyyUTuNlW94as0h+ocEcuv0YXZH8RlaCPzAwqmpHCyuJetIhd1RlHJLbmkd7+04xnenDSVGR9f1GC0EfuCacxKJCA3ipS+101h5t6c/PURQYACLL0izO4pP0ULgB/qHBLFwairv7Tim4w8pr1VQ2cBbW/KZf24KCRFhdsfxKVoI/MRdM9OJ7hfMw+/v1b4C5ZWWfOa6w+33LxxhcxLfo4XAT0T1C+Ynl57FlzllfLK33RvJKdVnFdc0snxTHtdNTiIpup/dcXyOW4VARGJF5GMROWg9t3vnaBFxtLkpzYo289NEZKOIZIvI69bdzFQPWZCZyoj4AfzXyr00tzo730CpPmLZ54dpcTj54UXpdkfxSe4eEdwLrDLGjARWWa/b02CMmWg95rSZ/9/Ao8aYdKACWOxmHnUawYEB3HfVGA6X1vGyXm2svERlfTMvbzjC1Wcnkhanw0n0BHcLwVzgRWv6RVz3He4S6z7FFwMn7mPcre3VmZk5KoHz0+P486qDVNY32x1HqU49uSabumYHd83UvoGe4m4hGGSMKbSmjwODOlgvTESyRGSDiMyz5g0EKo0xJwbMzweS3MyjOiEi/PrqMdQ0tvD4qmy74yh1WtvzKlm27jALMlMZPTjS7jg+q9N7FovIJ8Dgdhbd1/aFMcaISEenoww1xhSIyHBgtXXD+m6dxygidwJ3AqSm6vgi7hg9OJKbzk3hpS9z+c60VIbHh9sdSalvaG518os3d5AQEcavrhxtdxyf1ukRgTFmljFmfDuPd4EiERkCYD23ezqKMabAes4BPgUmAWVAtIicKEbJQId3UTHGLDHGZBhjMuLj47uxi6o9P7n0LEKDAnjkg312R1GqXU99ms3+ohoevnY8kTqmUI9yt2loBbDIml4EvHvqCiISIyKh1nQcMAPYY1wns68Bbjjd9qpnJESEcdfMdD7aU8T6Q6V2x1Hqa/Yfr+HJNdnMnZjIJWM6anFWnuJuIXgEuFREDgKzrNeISIaILLXWGQNkich2XF/8jxhj9ljLfgn8VESycfUZLHMzj+qGxeenkRTdj4fe20uLQ08nVX1Dq8PJL97cTkRYMPdfM87uOH6h0z6C0zHGlAGXtDM/C7jdml4PTOhg+xwg050M6syFBQfym6vH8IOXt/CHD/fzqyvH2B1JKZ7/Ipft+VU8vmASsTqwXK/QK4v93OzxQ1g4NZVn1uawel+R3XGUn8streMPH+1n1phBXHO23ou4t2ghUPz26rGMHhzBz97YTmFVg91xlJ9yOg2/fGsHIUEBPHzteFyXGqneoIVAERYcyJM3T6ap1ck9r22lVfsLlA1e23SUjYfL+fVVYxgUqaOL9iYtBAqAEfHh/Ne1E9iUW8GfPj5gdxzlZwoqG/j9yn3MSB/IjRkpdsfxO1oI1EnzJiUx/9wUnvr0EJ8dKLE7jvITdU2t3PlSFsYYfn/t2dokZAMtBOpr7r9mHKMGRfDT17dRVN1odxzl4xxOw78t38bewmqeuHkyqQP72x3JL2khUF/TLySQJ2+eRH2zQ/sLVI/7/cq9fLK3iPuvGcfMUQl2x/FbWgjUN6QnRPDQvPFsPFzO46sO2h1H+aiXNxxh6brD3DJ9GIumD7M7jl/TQqDadf2UZG6Yksxf1mSzVvsLlIetPVDC/St2M3NUPL++Si9ktJsWAtWhB+a6+gt+8PJmNh8ptzuO8hEHimr40StbGJkQzl8WTiYoUL+G7Ka/AdWh/iFBvLQ4k8GRYdzy3Ca251XaHUl5uZKaJm59fhNhIYEsu+VcwkPdGuVGeYgWAnVaCRFhvHLHVKIHBPO9575i97Fu3UZCqZMaWxzc+bcsyuqaWPq9DL0JfR+ihUB1akhUP169fRoDQgL57rKvOFBUY3ck5WWcTsPP/76drUcreeymiZyTEm13JNWGFgLVJSmx/Xn1jmkEBQgLn91ITkmt3ZGUl3A6DQ+9v5f3dhRy7xWjmT1eB5Pra7QQqC4bFjeAV++YijGGhc9u5GhZvd2RVB/X4nDy879v57kvXKeJfv9bw+2OpNqhhUB1S3pCBC/fPpXGVgcLnt1AQaWOVqraV9/cyh0vZfH21gJ+dulZ3H/NWB0+oo9yqxCISKyIfCwiB63nmHbWmSki29o8GkVknrXsBRE53GbZRHfyqN4xZkgkf7ttKtWNLSx8doMORaG+oaKumYXPbmTtgRJ+f90EfnzJSC0CfZi7RwT3AquMMSOBVdbrrzHGrDHGTDTGTAQuBuqBj9qs8h8nlhtjtrmZR/WSCclRvHhbJqU1TSzQYqDaKKhs4Ia/rmdPYTVP3TyFBZmpdkdSnXC3EMwFXrSmXwTmdbL+DcAHxhhtXPYBk1NjeP7WTI5XNXLNX9ax+UiF3ZGUzQ4U1XD9U+sprmnib7dlMnv8YLsjqS5wtxAMMsYUWtPHgUGdrD8feO2UeQ+LyA4ReVREQjvaUETuFJEsEckqKdEhD/qKzLRY3r5rOmHBgcxf8iWvbjxqdyRlk6zccm54ej0OY3jj++cxdfhAuyOpLhJjzOlXEPkEaK+s3we8aIyJbrNuhTHmG/0E1rIhwA4g0RjT0mbecSAEWAIcMsY80FnojIwMk5WV1dlqqhdV1jdzz/JtrD1QwoLMFH43ZxyhQYF2x1K95JM9Rfzo1S0kRvfjpdsySYnV4aT7IhHZbIzJOHV+p9d3G2NmneZNi0RkiDGm0PpSLz7NW90I/ONEEbDe+8TRRJOIPA/8vLM8qm+K7h/C87ecyx8/2s9Tnx5i3/Ea/vqdKXrLQT/wxqY8fvWPnYxLjOT5W85lYHiHB/aqj3K3aWgFsMiaXgS8e5p1F3BKs5BVPBDX6QTzgF1u5lE2CgwQfjF7NE/dPJn9x2u4+i/ryMrVwep8VXVjCz95fRu/eGsH00cM5NU7pmkR8FLuFoJHgEtF5CAwy3qNiGSIyNITK4nIMCAF+OyU7V8RkZ3ATiAOeMjNPKoPuHLCEN750QwGhAQyf8kG/rbhCJ01QSrvsiGnjCse+5wV24/xb5eM5DkdQM6rddpH0BdpH4F3qGpo4d+Xb2XN/hJuzEjmgbnjCQvWfgNv1tTq4I8fHeDZz3MYGtufR2+ayKTUdrsFVR90xn0ESp2pqH7BLFt0Lo99coDHV2ez/3gNj940keHx4XZHU2dg3/Fq/n35NvYdr2Hh1FR+fdUY+ofoV4gv0CEmVI8KCBB+etkonvnuFHJK65j92Of88aP9NDQ77I6musjpNDy7Noc5f/mC0tomnrslg/+6doIWAR+iv0nVKy4fN5hJqdH8fuU+/rI6m39sLeB314xj1tjOLj1RdiqobOBnb2xjQ045l44dxCPXTdAOYR+kfQSq1315qIzfvruLg8W1zBoziPuvGavnnfcxxhje3XaM37y7C6fTcP814/h2RrKOF+TlOuoj0EKgbNHicPLcusP8edVBnMZw98x07vjWcL0IrQ/YfKSc//1wPxtyypkyNIZHb5xI6kAt1L5AC4Hqk45VNvDQ+3tYufM4w+MG8J9zx3HByHi7Y/ml3ceq+ONHB1i9r5i48BDunpnOd6YN1ZvL+xAtBKpP++xACfe/u4vcsnquOnsIv7lqLIOj9Krk3nCopJY/fXyA93cUEhkWxPcvHMGtM4ZpZ7AP0kKg+rzGFgdL1ubw5JpsAkS4MSOZW2ekMSxugN3RfFJ+RT2PrzrIm5vzCQsO5LYZadzxreFE9Qu2O5rqIVoIlNc4WlbPn1cd5J/bj9HidHLJ6EEsPj+NacNjtbPSA4prGnlqzaGTI8V+Z9pQ7po5gjg9G8jnaSFQXqe4ppGXvzzCyxuPUl7XzLjESBafn8bVZycSEqTt1t1VVtvE0nWHeeGLXJodTm7MSObHF48kMbqf3dFUL9FCoLxWY4uDf2wtYNm6w2QX15IQEcqi6cNYmJlKzIAQu+P1aU2tDlbvLeatLQV8ur8YhzHMOSeRf591Fmna5OZ3tBAor2eM4bMDJSxbd5jPD5YSFhzAdZOTuW1GGukJOmzFCcYYtuZV8vaWfP65vZCqhhYSIkK5dlIS385IJj0hwu6IyiY61pDyeiLCRaMSuGhUAgeKanhu3WHe3JzPqxuPMjUtllljBnHxmASGxw3wy76E/Ip63tlawNtbCsgprSMsOIDLxw3musnJnJ8eR2CA//1MVNfoEYHyaqW1Tby68Sgrdxay73gNAMMG9ufi0YO4ZEwC5w6L9en+hNqmVlbuLOTtLflsyHHd+2Ha8Fium5zMFeMHExGmZwCpf9GmIeXz8ivqWbOvmFX7ill/qIzmVifhoUF866w4Lh49iItGxXv9mTG1Ta1sz6tk85EKso5U8NXhMhpbnKTFDeC6SUnMm5Skw3WoDmkhUH6lvrmVL7LLWL2viFV7iymuaUIEJqZEc8noBKanxzEyIbxP/8VsjKGgsoHNRypOPvYWVuM0IAKjBkUwNS2WuZOSmJQS7ZfNYap7eqQQiMi3gd8BY4BMY0y7384iMhv4MxAILDXGnLiTWRqwHBgIbAa+a4xp7uxztRCo7jDGsPtYNav2FrN6XxHb86tOLhscGUZ6QvjJx0jr2Y4RNptaHewrrCHrSAVbjlSQdaScouomAAaEBDIpNYbJQ2OYMjSGSanRRPbhIqb6pp4qBGMAJ/AM8PP2CoGIBAIHgEuBfGATsMAYs0dE3gDeNsYsF5G/AtuNMU939rlaCJQ7imsa2Xa0kuySWrKL//Wob3OPhJj+wYxMiGCEVRxGJIQTGRZEaFAgocEBhAUHEhoUYD0CCQ6Udv8iN8ZQ29RKcU0TJTVNFNc0UVzdSEltEyXV1uuaRkpqmqiobzm5XVJ0PzKGub70pwyNYdSgCB3zR7mtR84aMsbstd78dKtlAtnGmBxr3eXAXBHZC1wMLLTWexHX0UWnhUApdyREhHHZuMFc1mae02korG4ku7iWg0U1HLKKxAe7CnmtzRd0RwKEk0XiRHEwGEprmmlo+eZNeEICA4iPCCU+IpRhAweQmRZLfLjr6GTK0BgdZ0n1qt44fTQJyGvzOh+Yiqs5qNIY09pmflJHbyIidwJ3AqSmpvZMUuW3AgKEpOh+JEX348Kz/jX6qTGGsrpmckrqqGtqpanVQVOrk6YWJ02tDhqt56ZWpzX/X9NOY4gLDyUhIpSEyFDiw8NIiHS9juoXrG36qs/otBCIyCfA4HYW3WeMedfzkdpnjFkCLAFX01Bvfa7ybyJCXHio159tpNTpdFoIjDGz3PyMAiClzetka14ZEC0iQdZRwYn5SimlelFv9D5tAkaKSJqIhADzgRXG1Uu9BrjBWm8R0GtHGEoppVzcKgQicq2I5APnAe+LyIfW/EQRWQlg/bV/N/AhsBd4wxiz23qLXwI/FZFsXH0Gy9zJo5RSqvv0gjKllPITHZ0+qicmK6WUn9NCoJRSfk4LgVJK+TktBEop5ee8srNYREqAIx56uzig1EPvZRdf2Afwjf3whX0A39gP3YdvGmqMiT91plcWAk8Skaz2etG9iS/sA/jGfvjCPoBv7IfuQ9dp05BSSvk5LQRKKeXntBBYA9l5OV/YB/CN/fCFfQDf2A/dhy7y+z4CpZTyd3pEoJRSfk4LgVJK+Tm/KwQi8m0R2S0iThHp8LQsEckVkZ0isk1E+tQId93Yh9kisl9EskXk3t7M2BUiEisiH4vIQes5poP1HNbvYZuIrOjtnO3p7GcrIqEi8rq1fKOIDLMh5ml1YR9uEZGSNj/72+3IeToi8pyIFIvIrg6Wi4g8bu3jDhGZ3NsZu6IL+3GRiFS1+V381qMBjDF+9QDGAKOAT4GM06yXC8TZnfdM9wEIBA4Bw4EQYDsw1u7sp2T8H+Bea/pe4L87WK/W7qzd/dkCdwF/tabnA6/bnfsM9uEW4Am7s3ayH98CJgO7Olh+JfABIMA0YKPdmc9wPy4C3uupz/e7IwJjzF5jzH67c7iji/uQCWQbY3KMMc3AcmBuz6frlrnAi9b0i8A8+6J0S1d+tm337U3gEulbNyn2hn8fnTLGrAXKT7PKXOAl47IB110Rh/ROuq7rwn70KL8rBN1ggI9EZLOI3Gl3mDOQBOS1eZ1vzetLBhljCq3p48CgDtYLE5EsEdkgIvN6J9ppdeVne3Id47o5UxWumy/1FV3993G91aTypoiktLO8r/OG/wdddZ6IbBeRD0RknCffuNN7FnsjEfkEGNzOovuMMV29Heb5xpgCEUkAPhaRfVbV7hUe2gfbnW4/2r4wxhgR6ehc5qHW72I4sFpEdhpjDnk6q/qGfwKvGWOaROT7uI5wLrY5k7/aguv/Qa2IXAm8A4z01Jv7ZCEwxszywHsUWM/FIvIPXIfSvVYIPLAPBUDbv+CSrXm96nT7ISJFIjLEGFNoHa4Xd/AeJ34XOSLyKTAJV/u2Xbrysz2xTr6IBAFRQFnvxOuSTvfBGNM271JcfTrepk/8P3CXMaa6zfRKEXlKROKMMR4ZkE6bhtohIgNEJOLENHAZ0G5vfh+2CRgpImkiEoKrw7JPnHHTxgpgkTW9CPjGkY6IxIhIqDUdB8wA9vRawvZ15Wfbdt9uAFYbq9evj+h0H05pS5+D657j3mYF8D3r7KFpQFWb5kivISKDT/QxiUgmru9uz/1hYXdveW8/gGtxtRM2AUXAh9b8RGClNT0c11kU24HduJpjbM/enX2wXl8JHMD113Of2gcr30BgFXAQ+ASIteZnAEut6enATut3sRNYbHfujn62wAPAHGs6DPg7kA18BQy3O/MZ7MPvrX//24E1wGi7M7ezD68BhUCL9X9iMfAD4AfWcgGetPZxJ6c5U7CP78fdbX4XG4Dpnvx8HWJCKaX8nDYNKaWUn9NCoJRSfk4LgVJK+TktBEop5ee0ECillJ/TQqCUUn5OC4FSSvm5/w9ISGteypAYhgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Create figure window\n", "plt.figure()\n", "\n", "# Plot regions \n", "theta = np.linspace(0,2*np.pi)\n", "X = np.cos(theta)\n", "Y = np.sin(theta)\n", "plt.plot(X,Y)\n", "plt.axis('equal')\n", "\n", "# Show plot\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.2 Convex Quadratics\n", "Consider a convex quadratic of the form\n", "\n", "$\n", "\\begin{align}\n", "f(x) = \\frac{1}{2} (ax_1^2 + bx_2^2)\n", "\\end{align}\n", "$\n", "\n", "for $a,b > 0$.\n", "\n", "#### Coding Task:\n", "\n", "Plot the contours of $f(x)$ above using Matplotlib's plt.contour." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Scaling parameters\n", "a = 10\n", "b = 1\n", "\n", "# Objective function and gradient\n", "fun = lambda x: 0.5*(a*x[0]**2+b*x[1]**2)\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-1,1)\n", "Y = np.linspace(-a,a)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercises:\n", "\n", "1. Calculate the gradient and Hessian of $f(x)$. \n", "\n", "2. Recall that $f(x)$ is Lipschitz continuous in $X$ if there exists a $\\gamma > 0$ such that for all $x,y \\in X$:\n", "\n", " $\n", " \\lvert f(x) - f(y) \\rvert \\le \\gamma \\lVert x - y \\rVert_2 \n", " $\n", "\n", " Is the convex quadratic $f(x)$ above Lipschitz continuous when $X=[\\alpha,\\beta]^2$? \n", " What about when $X = \\mathbb{R}^2$? You may find it helpful to plot $f(x)$ in 1D.\n", "\n", "3. Similarly, $\\nabla f(x)$ is Lipschitz continuous in $X$ if there exists a $\\gamma > 0$ such that for all $x,y \\in X$:\n", "\n", " $\n", " \\lVert \\nabla f(x) - \\nabla f(y) \\rVert_2 \\le \\gamma \\lVert x - y \\rVert_2 \n", " $\n", "\n", " Is the gradient $\\nabla f(x)$ Lipschitz continuous when $X=[\\alpha,\\beta]^2$? What about when $X = \\mathbb{R}^2$?\n", "\n", "4. Similarly, is the Hessian $\\nabla^2 f(x)$ Lipschitz continuous?\n", "\n", "\n", "#### Answeres:\n", "\n", "The gradient for this problem is\n", "\n", "$\n", "\\begin{align}\n", "\\nabla f(x) = \n", "\\begin{pmatrix}\n", "a x_1 \\\\\n", "b x_2\n", "\\end{pmatrix}\n", "\\end{align}\n", "$\n", "\n", "The Hessian for this problem is\n", "\n", "$\n", "\\begin{align}\n", "\\nabla^2 f(x) = \n", "\\begin{pmatrix}\n", "a & 0 \\\\\n", "0 & b\n", "\\end{pmatrix} \n", "\\succ 0\n", "\\end{align}\n", "$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.3 Rosenbrock Function\n", "Consider the Rosenbrock function defined as\n", "\n", "$\n", "f(x) = (a - x_1)^2 + b(x_2 - x_1^2)^2\n", "$\n", "\n", "where usually $a=1$ and $b=100$.\n", "\n", "#### Coding Task:\n", "\n", "Plot the contours of $f(x)$ above using Matplotlib's plt.contour. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Parameters\n", "a = 1\n", "b = 100\n", "\n", "# Objective function and gradient\n", "fun = lambda x: (a-x[0])**2 + b*(x[1]-x[0]**2)**2\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-2,2)\n", "Y = np.linspace(-2,2)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercises: \n", "1. Calculate the gradient and Hessian of this function.\n", "\n", "#### Answers:\n", "The gradient for this function is\n", "\n", "$\n", "\\begin{align}\n", "\\nabla f(x) = \n", "\\begin{pmatrix}\n", "-2(a - x_1) -2x_1 2b(x_2 - x_1^2) \\\\\n", "2b(x_2 - x_1^2)\n", "\\end{pmatrix}\n", "\\end{align}\n", "$\n", "\n", "The Hessian for this function is\n", "\n", "$\n", "\\begin{align}\n", "\\nabla^2 f(x) = \n", "\\begin{pmatrix}\n", "2 -4bx_2 +12bx_1^2 & -4bx_1 \\\\\n", "-4bx_1 & 2b\n", "\\end{pmatrix}\n", "\\end{align}\n", "$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.8.7" } }, "nbformat": 4, "nbformat_minor": 4 }