1D Optimization Homework using the Secant Method - An Introduction to Optimization for Engineers.ipynb

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   "source": [
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
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    {
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       "  ⋮\n",
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     "execution_count": 6,
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     "output_type": "execute_result"
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   "source": [
    "x = LinRange(-pi, 4*pi, 501)\n",
    "f = sin.(x) .- ((x.^2)/10) + x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
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       "  1747.89,230.103 1752.06,238.085 1756.23,246.258 1760.4,254.618 1764.58,263.161 1768.75,271.884 1772.92,280.781 1777.09,289.849 1781.26,299.084 1785.43,308.479 \n",
       "  1789.6,318.032 1793.78,327.737 1797.95,337.588 1802.12,347.582 1806.29,357.712 1810.46,367.974 1814.63,378.361 1818.8,388.87 1822.98,399.494 1827.15,410.227 \n",
       "  1831.32,421.064 1835.49,432 1839.66,443.028 1843.83,454.142 1848.01,465.337 1852.18,476.607 1856.35,487.945 1860.52,499.346 1864.69,510.804 1868.86,522.313 \n",
       "  1873.03,533.866 1877.21,545.458 1881.38,557.083 1885.55,568.733 1889.72,580.405 1893.89,592.09 1898.06,603.785 1902.23,615.481 1906.41,627.174 1910.58,638.858 \n",
       "  1914.75,650.526 1918.92,662.174 1923.09,673.794 1927.26,685.382 1931.44,696.933 1935.61,708.439 1939.78,719.897 1943.95,731.3 1948.12,742.644 1952.29,753.923 \n",
       "  1956.46,765.132 1960.64,776.266 1964.81,787.321 1968.98,798.291 1973.15,809.173 1977.32,819.961 1981.49,830.651 1985.66,841.239 1989.84,851.721 1994.01,862.093 \n",
       "  1998.18,872.351 2002.35,882.491 2006.52,892.511 2010.69,902.407 2014.86,912.174 2019.04,921.812 2023.21,931.316 2027.38,940.685 2031.55,949.915 2035.72,959.004 \n",
       "  2039.89,967.95 2044.07,976.751 2048.24,985.406 2052.41,993.912 2056.58,1002.27 2060.75,1010.48 2064.92,1018.53 2069.09,1026.43 2073.27,1034.18 2077.44,1041.77 \n",
       "  2081.61,1049.21 2085.78,1056.5 2089.95,1063.63 2094.12,1070.61 2098.29,1077.43 2102.47,1084.1 2106.64,1090.62 2110.81,1096.99 2114.98,1103.21 2119.15,1109.28 \n",
       "  2123.32,1115.2 2127.5,1120.98 2131.67,1126.62 2135.84,1132.11 2140.01,1137.47 2144.18,1142.69 2148.35,1147.78 2152.52,1152.73 2156.7,1157.56 2160.87,1162.27 \n",
       "  2165.04,1166.85 2169.21,1171.32 2173.38,1175.67 2177.55,1179.92 2181.72,1184.05 2185.9,1188.09 2190.07,1192.03 2194.24,1195.87 2198.41,1199.62 2202.58,1203.29 \n",
       "  2206.75,1206.88 2210.93,1210.4 2215.1,1213.85 2219.27,1217.23 2223.44,1220.55 2227.61,1223.82 2231.78,1227.04 2235.95,1230.21 2240.13,1233.35 2244.3,1236.45 \n",
       "  2248.47,1239.53 2252.64,1242.59 2256.81,1245.63 2260.98,1248.66 2265.15,1251.69 2269.33,1254.72 2273.5,1257.76 2277.67,1260.81 2281.84,1263.89 2286.01,1266.99 \n",
       "  2290.18,1270.12 \n",
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       "</svg>\n"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(x,f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "zeroth_derivative (generic function with 1 method)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function zeroth_derivative(x)\n",
    "    \n",
    "    return sin(x) + x - ((x^2)/10)\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "first_derivative (generic function with 1 method)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function first_derivative(x)\n",
    "    \n",
    "    return cos(x) + 1 - (x/5)\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "second_derivative (generic function with 1 method)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function second_derivative(x)\n",
    "    \n",
    "    return -sin(x)-(1/5)\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 4\n",
    "dx = 0.01\n",
    "\n",
    "for iteration = 1:100\n",
    "    \n",
    "    numerator = (zeroth_derivative(x+dx) - zeroth_derivative(x-dx))/(2*dx)\n",
    "    \n",
    "    denominator = (zeroth_derivative(x+dx) - 2*zeroth_derivative(x) + zeroth_derivative(x-dx))/(dx^2)\n",
    "    \n",
    "    x = x - numerator/denominator\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.640407045804283"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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