# AMPL Model by Hande Y. Benson # # Copyright (C) 2001 Princeton University # All Rights Reserved # # Permission to use, copy, modify, and distribute this software and # its documentation for any purpose and without fee is hereby # granted, provided that the above copyright notice appear in all # copies and that the copyright notice and this # permission notice appear in all supporting documentation. # Source: # Francois Grondin (francois.grondin@qc.forintek.ca) # Forintek Canada Corp, 319, rue Franquet, Quebec, G1P 4R4, CANADA # SIF input: Nick Gould, Dec 1997. # classification QOR2-AN-583-774 param n := 195; param R := 2500; param x{0..n}; param y{0..n}; param dx := x[15]-x[0]; param dy := y[15]-y[0]; param m_0:= dy/dx; param m := 4; var a{0..m}; var p{0..n}; var pprime{0..n}; var pprime2{0..n}; minimize f: sum {j in 0..n} (p[j]-y[j])^2; subject to cons1{j in 0..n}: sum {i in 0..m} (a[i]*x[j]^i)-p[j] = 0; subject to cons2{j in 0..n}: sum {i in 1..m} (a[i]*i*x[j]^(i-1))-pprime[j] = 0; subject to cons3{j in 0..n}: sum {i in 2..m} (a[i]*i*(i-1)*x[j]^(i-2))-pprime2[j] = 0; subject to cons4{j in 0..n}: R^2*pprime2[j]^2-(1+pprime[j]^2)^3 <= 0; subject to cons5: p[0] = y[0]; subject to cons6: pprime[0] = m_0; data; param : x y:= 0 0.0 3.556 1 2.54 3.56346 2 5.08 3.57091 3 7.62001 3.57837 4 10.1612 3.59371 5 12.7012 3.60213 6 15.2412 3.61055 7 17.7812 3.61898 8 20.3212 3.6274 9 22.8612 3.63582 10 25.4012 3.6423 11 27.9412 3.65073 12 30.4812 3.6653 13 33.0212 3.67381 14 35.5612 3.68233 15 38.1012 3.69084 16 40.6411 3.50637 17 43.1811 3.51498 18 45.7231 2.77481 19 48.2631 2.78376 20 50.8031 2.79272 21 53.3431 2.80168 22 55.8839 2.78529 23 58.4239 2.79415 24 60.965 2.47602 25 63.505 2.48617 26 66.045 2.48369 27 68.585 2.49377 28 71.125 2.27635 29 73.665 2.28521 30 76.205 2.26744 31 78.745 2.27605 32 81.285 2.28465 33 83.825 2.29325 34 86.365 2.4907 35 88.905 2.49921 36 91.445 2.50773 37 93.985 2.51624 38 96.525 2.53381 39 99.065 2.54241 40 101.605 2.74855 41 104.145 2.75716 42 106.685 2.76576 43 109.225 2.77437 44 111.766 2.60758 45 114.306 2.6161 46 116.847 2.26008 47 119.387 2.2686 48 121.927 2.28695 49 124.467 2.29556 50 127.008 1.47808 51 129.548 1.4854 52 132.09 1.1101 53 134.63 1.1188 54 137.17 1.12749 55 139.71 1.13619 56 142.251 0.978377 57 144.791 0.987075 58 147.33 0.82203 59 149.87 0.829676 60 152.41 0.837322 61 154.95 0.844885 62 157.49 0.852781 63 160.03 0.86051 64 162.571 0.538377 65 165.111 0.546996 66 167.651 0.600516 67 170.191 0.609224 68 172.731 0.789128 69 175.271 0.798084 70 177.811 1.00996 71 180.351 1.01883 72 182.891 1.03712 73 185.431 1.04591 74 187.972 0.720837 75 190.512 0.699625 76 193.052 0.708414 77 195.592 0.717203 78 198.133 0.609086 79 200.673 0.617627 80 203.213 0.199369 81 205.753 0.207992 82 208.293 0.225288 83 210.833 0.233831 84 213.374 -0.172432 85 215.914 -0.163889 86 218.456 -0.34889 87 220.996 -0.341233 88 223.536 -0.333576 89 226.076 -0.32592 90 228.616 -0.522016 91 231.156 -0.514426 92 233.696 -0.506837 93 236.236 -0.499248 94 238.776 -0.491658 95 241.316 -0.484069 96 243.856 -0.47648 97 246.396 -0.46889 98 248.936 -0.462453 99 251.476 -0.455008 100 254.016 -0.447563 101 256.556 -0.440118 102 259.095 0.055237 103 261.635 0.063873 104 264.176 0.062826 105 266.716 0.070575 106 269.256 -0.275144 107 271.797 -0.275842 108 274.337 -0.268089 109 276.877 -0.260335 110 279.417 -0.118406 111 281.957 -0.110665 112 284.497 -0.102923 113 287.037 -0.095181 114 289.577 0.103362 115 292.117 0.111028 116 294.657 0.131239 117 297.197 0.138981 118 299.736 0.27243 119 302.276 0.280024 120 304.815 0.421614 121 307.355 0.429144 122 309.895 0.436674 123 312.435 0.444203 124 314.976 0.484027 125 317.516 0.491804 126 320.056 0.515482 127 322.598 0.571256 128 325.138 0.580224 129 327.678 0.589193 130 330.215 1.11182 131 332.755 1.12071 132 335.295 1.34551 133 337.835 1.35448 134 340.375 1.38382 135 342.915 1.39287 136 345.454 1.77298 137 347.994 1.78202 138 350.534 2.00633 139 353.074 2.01544 140 355.615 2.41293 141 358.155 2.42093 142 360.695 2.39029 143 363.235 2.39823 144 365.773 2.89123 145 368.313 2.89911 146 370.853 3.33714 147 373.393 3.34509 148 375.933 3.40441 149 378.473 3.41248 150 381.012 3.70271 151 383.552 3.71094 152 386.09 4.15353 153 388.632 4.12735 154 391.17 4.56011 155 393.71 4.56923 156 396.25 4.77252 157 398.79 4.78163 158 401.329 4.89149 159 403.869 4.89935 160 406.41 4.96478 161 408.95 4.97272 162 411.49 5.16767 163 414.03 5.17553 164 416.57 5.38577 165 419.11 5.39364 166 421.65 5.40151 167 424.19 5.40937 168 426.729 5.28358 169 429.269 5.29136 170 431.81 5.14203 171 434.35 5.14865 172 436.891 4.80067 173 439.431 4.80729 174 441.972 4.86169 175 444.512 4.86947 176 447.052 4.56159 177 449.592 4.56937 178 452.134 3.78824 179 454.674 3.79602 180 457.214 3.8038 181 459.754 3.81158 182 462.295 3.66534 183 464.835 3.67306 184 467.375 3.67665 185 469.915 3.6845 186 472.455 3.6904 187 474.995 3.69832 188 477.535 3.70624 189 480.075 3.71416 190 482.616 3.50154 191 485.156 3.50963 192 487.696 3.51772 193 490.236 3.52581 194 492.776 3.5339 195 495.316 3.54199; solve; display f; #display p, pprime, pprime2, a;