Unconstrained Optimization (Trust Region)Last updated: 01/01/2023

  1. Problem: name of the benchmark problem.
  2. f(x): objective function value at solution.
  3. eps(C): convergency tolerance.
  4. eps(F): feasibility tolerance.
  5. # Iter.: number of iterations used by the solver.
  6. # x: number of variables in the benchmark problem.
  7. # b: number of simple bound constraints in the benchmark problem.
  8. # LC: number of linear constraints in the benchmark problem.
  9. # NLC: number of non-linear constraints in the benchmark problem.
  10. # f(x)-O: number of function calls used by the solver to evaluate objective function.
  11. # g(x)-O: number of function calls used by the solver to evaluate the gradient of the objective function.
  12. # H(x)-O: number of function calls used by the solver to evaluate the Hessian of the objective function.
  13. # f(x)-C: number of function calls used by the solver to evaluate the nonlinear constraint function.
  14. # g(x)-C: number of function calls used by the solver to evaluate the gradient of the nonlinear constraint function.
  15. Time(ms.): time in milliseconds used by the solver to find the solution.

CUTE unconstrained optimization benchmark problems.

  • Method choice: Trust region - Exact
  • Max number of iterations:5000
Problem f(x) eps(C) eps(F) # Iter. # x # b # LC # NLC # f(x)-O # g(x)-O # H(x)-O # f(x)-C # g(x)-C Time(ms.)
AKIVA 6.166e+000 1.0e-007 0.0e+000 6 2 0 0 0 13 7 7 0 0 164.6
ALLINITU 5.744e+000 1.0e-007 0.0e+000 11 4 0 0 0 20 9 9 0 0 286.1
BARD 8.215e-003 1.0e-007 0.0e+000 7 3 0 0 0 15 8 8 0 0 183.4
BEALE 8.130e-029 1.0e-007 0.0e+000 10 2 0 0 0 18 8 8 0 0 164.8
BIGGS6 3.749e-017 1.0e-007 0.0e+000 39 6 0 0 0 70 31 31 0 0 178.9
BOX3 1.793e-017 1.0e-007 0.0e+000 12 3 0 0 0 22 10 10 0 0 183.1
BRKMCC 1.690e-001 1.0e-007 0.0e+000 3 2 0 0 0 7 4 4 0 0 96.6
BROWNBS 1.972e-031 1.0e-007 0.0e+000 14 2 0 0 0 29 15 15 0 0 169.2
BROWNDEN 8.582e+004 1.0e-007 0.0e+000 8 4 0 0 0 17 9 9 0 0 195.8
CLIFF 1.998e-001 1.0e-007 0.0e+000 27 2 0 0 0 55 28 28 0 0 161.9
CUBE 1.917e-020 1.0e-007 0.0e+000 34 2 0 0 0 64 30 30 0 0 159.2
DENSCHNA 1.103e-023 1.0e-007 0.0e+000 6 2 0 0 0 13 7 7 0 0 167.8
DENSCHNB 1.180e-020 1.0e-007 0.0e+000 8 2 0 0 0 14 6 6 0 0 200.1
DENSCHNC 2.178e-020 1.0e-007 0.0e+000 10 2 0 0 0 21 11 11 0 0 154.4
DENSCHND 3.927e-012 1.0e-007 0.0e+000 41 3 0 0 0 83 42 42 0 0 185.8
DENSCHNE 2.213e-028 1.0e-007 0.0e+000 22 3 0 0 0 39 17 17 0 0 162.3
DENSCHNF 6.513e-022 1.0e-007 0.0e+000 6 2 0 0 0 13 7 7 0 0 177.2
DJTL -8.952e+003 1.0e-007 0.0e+000 87 2 0 0 0 145 57 57 0 0 164.3
ENGVAL2 1.406e-020 1.0e-007 0.0e+000 22 3 0 0 0 40 18 18 0 0 213.0
EXPFIT 2.405e-001 1.0e-007 0.0e+000 16 2 0 0 0 28 12 12 0 0 158.4
GROWTHLS 1.004e+000 1.0e-007 0.0e+000 86 3 0 0 0 161 75 75 0 0 207.4
GULF 2.283e-024 1.0e-007 0.0e+000 34 3 0 0 0 63 29 29 0 0 214.3
HAIRY 2.000e+001 1.0e-007 0.0e+000 59 2 0 0 0 109 50 50 0 0 161.5
HATFLDD 2.547e-007 1.0e-007 0.0e+000 32 3 0 0 0 59 27 27 0 0 193.3
HATFLDE 6.533e-005 1.0e-007 0.0e+000 26 3 0 0 0 50 24 24 0 0 199.2
HATFLDFL 6.050e-005 1.0e-007 0.0e+000 126 3 0 0 0 239 113 113 0 0 208.3
HEART6LS 1.577e-025 1.0e-007 0.0e+000 217 6 0 0 0 413 196 196 0 0 253.6
HEART8LS 6.899e-025 1.0e-007 0.0e+000 106 8 0 0 0 193 87 87 0 0 228.7
HELIX 1.337e-033 1.0e-007 0.0e+000 12 3 0 0 0 23 11 11 0 0 198.7
HIELOW 8.742e+002 1.0e-007 0.0e+000 7 3 0 0 0 13 6 6 0 0 297.8
HIMMELBB 2.392e-012 1.0e-007 0.0e+000 24 2 0 0 0 49 25 25 0 0 168.0
HIMMELBF 3.186e+002 1.0e-007 0.0e+000 50 4 0 0 0 99 49 49 0 0 201.1
HIMMELBG 3.671e-017 1.0e-007 0.0e+000 11 2 0 0 0 18 7 7 0 0 188.6
HIMMELBH -1.000e+000 1.0e-007 0.0e+000 8 2 0 0 0 14 6 6 0 0 173.5
HUMPS 4.980e-017 1.0e-007 0.0e+000 2150 2 0 0 0 4147 1997 1997 0 0 303.8
HYDC20LS 5.878e-004 1.0e-007 0.0e+000 5000 99 0 0 0 8837 3837 3837 0 0 117900.0
JENSMP 1.244e+002 1.0e-007 0.0e+000 9 2 0 0 0 20 10 10 0 0 187.1
KOWOSB 3.078e-004 1.0e-007 0.0e+000 16 4 0 0 0 26 10 10 0 0 192.6
LOGHAIRY 1.823e-001 1.0e-007 0.0e+000 2952 2 0 0 0 5867 2915 2915 0 0 314.0
MARATOSB -1.000e+000 1.0e-007 0.0e+000 731 2 0 0 0 1424 693 693 0 0 227.6
MEXHAT -4.001e-002 1.0e-007 0.0e+000 31 2 0 0 0 60 29 29 0 0 169.9
MEYER3 8.795e+001 1.0e-007 0.0e+000 306 3 0 0 0 555 248 248 0 0 236.7
OSBORNEA 5.465e-005 1.0e-007 0.0e+000 29 5 0 0 0 58 29 29 0 0 207.0
OSBORNEB 4.014e-002 1.0e-007 0.0e+000 18 11 0 0 0 33 15 15 0 0 214.8
PALMER1C 9.761e-002 1.0e-007 0.0e+000 4 8 0 0 0 9 5 5 0 0 206.1
PALMER1D 6.527e-001 1.0e-007 0.0e+000 4 7 0 0 0 9 5 5 0 0 191.9
PALMER2C 1.437e-002 1.0e-007 0.0e+000 2 8 0 0 0 5 3 3 0 0 152.3
PALMER3C 1.954e-002 1.0e-007 0.0e+000 2 8 0 0 0 5 3 3 0 0 208.4
PALMER4C 5.031e-002 1.0e-007 0.0e+000 2 8 0 0 0 5 3 3 0 0 194.2
PALMER5C 2.128e+000 1.0e-007 0.0e+000 1 6 0 0 0 3 2 2 0 0 193.2
PALMER6C 1.639e-002 1.0e-007 0.0e+000 4 8 0 0 0 9 5 5 0 0 195.4
PALMER7C 6.020e-001 1.0e-007 0.0e+000 7 8 0 0 0 15 8 8 0 0 199.6
PALMER8C 1.598e-001 1.0e-007 0.0e+000 5 8 0 0 0 11 6 6 0 0 201.7
PARKCH 1.624e+003 1.0e-007 0.0e+000 18 15 0 0 0 33 15 15 0 0 11990.0
ROSENBR 2.069e-023 1.0e-007 0.0e+000 28 2 0 0 0 52 24 24 0 0 176.0
S308 7.732e-001 1.0e-007 0.0e+000 11 2 0 0 0 22 11 11 0 0 186.1
SINEVAL 6.920e-017 1.0e-007 0.0e+000 55 2 0 0 0 101 46 46 0 0 158.0
SISSER 1.623e-011 1.0e-007 0.0e+000 16 2 0 0 0 33 17 17 0 0 156.3
SNAIL 1.382e-025 1.0e-007 0.0e+000 73 2 0 0 0 139 66 66 0 0 167.4
STRATEC -2.461e+004 1.0e-007 0.0e+000 15 10 0 0 0 19 3 3 0 0 1561.0
TOINTGOR 1.374e+003 1.0e-007 0.0e+000 7 50 0 0 0 15 8 8 0 0 248.0
TOINTPSP 2.256e+002 1.0e-007 0.0e+000 19 50 0 0 0 36 17 17 0 0 333.1
TOINTQOR 1.175e+003 1.0e-007 0.0e+000 1 50 0 0 0 3 2 2 0 0 201.4
VIBRBEAM 1.564e-001 1.0e-007 0.0e+000 43 8 0 0 0 82 38 38 0 0 216.8
YFITU 6.670e-013 1.0e-007 0.0e+000 50 3 0 0 0 93 43 43 0 0 191.7
ZANGWIL2 -1.820e+001 1.0e-007 0.0e+000 1 2 0 0 0 3 2 2 0 0 154.9

CUTE unconstrained optimization benchmark problems.

  • Method choice: Trust region - Steihaug
  • Max number of iterations:5000
Problem f(x) eps(C) eps(F) # Iter. # x # b # LC # NLC # f(x)-O # g(x)-O # H(x)-O # f(x)-C # g(x)-C Time(ms.)
AKIVA 6.166e+000 1.0e-007 0.0e+000 10 2 0 0 0 21 11 11 0 0 88.8
ALLINITU 5.744e+000 1.0e-007 0.0e+000 23 4 0 0 0 44 20 20 0 0 71.0
BARD 8.215e-003 1.0e-007 0.0e+000 18 3 0 0 0 36 18 18 0 0 75.5
BEALE 9.464e-027 1.0e-007 0.0e+000 15 2 0 0 0 30 15 15 0 0 71.1
BIGGS6 5.587e-010 1.0e-007 0.0e+000 305 6 0 0 0 578 273 273 0 0 139.3
BOX3 1.804e-015 1.0e-007 0.0e+000 12 3 0 0 0 25 13 13 0 0 70.6
BRKMCC 1.690e-001 1.0e-007 0.0e+000 4 2 0 0 0 9 5 5 0 0 72.3
BROWNBS 0.000e+000 1.0e-007 0.0e+000 20 2 0 0 0 41 21 21 0 0 128.9
BROWNDEN 8.582e+004 1.0e-007 0.0e+000 14 4 0 0 0 30 15 15 0 0 72.9
CLIFF 1.998e-001 1.0e-007 0.0e+000 27 2 0 0 0 55 28 28 0 0 69.0
CUBE 1.755e-021 1.0e-007 0.0e+000 41 2 0 0 0 78 37 37 0 0 84.6
DENSCHNA 1.264e-016 1.0e-007 0.0e+000 8 2 0 0 0 17 9 9 0 0 75.0
DENSCHNB 3.203e-016 1.0e-007 0.0e+000 10 2 0 0 0 21 11 11 0 0 76.5
DENSCHNC 9.362e-016 1.0e-007 0.0e+000 13 2 0 0 0 27 14 14 0 0 87.2
DENSCHND 1.090e-009 1.0e-007 0.0e+000 43 3 0 0 0 87 44 44 0 0 77.7
DENSCHNE 4.800e-019 1.0e-007 0.0e+000 21 3 0 0 0 38 17 17 0 0 80.1
DENSCHNF 2.616e-018 1.0e-007 0.0e+000 17 2 0 0 0 33 16 16 0 0 80.7
DJTL -8.952e+003 1.0e-007 0.0e+000 238 2 0 0 0 401 163 163 0 0 92.5
ENGVAL2 9.774e-017 1.0e-007 0.0e+000 26 3 0 0 0 50 24 24 0 0 76.0
EXPFIT 2.405e-001 1.0e-007 0.0e+000 18 2 0 0 0 32 14 14 0 0 77.9
GROWTHLS 1.004e+000 1.0e-007 0.0e+000 242 3 0 0 0 469 226 226 0 0 111.9
GULF 4.834e-015 1.0e-007 0.0e+000 65 3 0 0 0 124 59 59 0 0 127.4
HAIRY 2.000e+001 1.0e-007 0.0e+000 80 2 0 0 0 148 68 68 0 0 86.7
HATFLDD 6.615e-008 1.0e-007 0.0e+000 27 3 0 0 0 49 22 22 0 0 77.6
HATFLDE 5.120e-007 1.0e-007 0.0e+000 22 3 0 0 0 42 20 20 0 0 96.2
HATFLDFL 6.132e-005 1.0e-007 0.0e+000 215 3 0 0 0 412 197 197 0 0 106.5
HEART6LS 2.921e-014 1.0e-007 0.0e+000 2068 6 0 0 0 3998 1930 1930 0 0 345.4
HEART8LS 9.089e-025 1.0e-007 0.0e+000 178 8 0 0 0 339 161 161 0 0 110.2
HELIX 3.149e-016 1.0e-007 0.0e+000 24 3 0 0 0 46 22 22 0 0 75.6
HIELOW 8.742e+002 1.0e-007 0.0e+000 15 3 0 0 0 30 14 14 0 0 334.4
HIMMELBB 3.144e-017 1.0e-007 0.0e+000 20 2 0 0 0 41 21 21 0 0 77.5
HIMMELBF 3.186e+002 1.0e-007 0.0e+000 321 4 0 0 0 635 313 313 0 0 138.6
HIMMELBG 6.079e-017 1.0e-007 0.0e+000 17 2 0 0 0 30 13 13 0 0 82.2
HIMMELBH -1.000e+000 1.0e-007 0.0e+000 8 2 0 0 0 14 6 6 0 0 79.8
HUMPS 2.688e-015 1.0e-007 0.0e+000 2852 2 0 0 0 5330 2478 2478 0 0 275.6
HYDC20LS 1.437e+000 1.0e-007 0.0e+000 5000 99 0 0 0 10000 5000 5000 0 0 10770.0
JENSMP 1.244e+002 1.0e-007 0.0e+000 11 2 0 0 0 24 12 12 0 0 88.8
KOWOSB 3.078e-004 1.0e-007 0.0e+000 26 4 0 0 0 51 25 25 0 0 84.4
LOGHAIRY 4.973e+000 1.0e-007 0.0e+000 5000 2 0 0 0 9518 4518 4518 0 0 349.3
MARATOSB -1.000e+000 1.0e-007 0.0e+000 1734 2 0 0 0 3275 1541 1541 0 0 221.2
MEXHAT -4.001e-002 1.0e-007 0.0e+000 20 2 0 0 0 42 21 21 0 0 85.7
MEYER3 9.184e+001 1.0e-007 0.0e+000 951 3 0 0 0 1838 887 887 0 0 215.6
OSBORNEA 5.465e-005 1.0e-007 0.0e+000 90 5 0 0 0 177 87 87 0 0 99.8
OSBORNEB 4.014e-002 1.0e-007 0.0e+000 61 11 0 0 0 116 55 55 0 0 137.1
PALMER1C 9.761e-002 1.0e-007 0.0e+000 1337 8 0 0 0 2676 1338 1338 0 0 361.9
PALMER1D 6.527e-001 1.0e-007 0.0e+000 50 7 0 0 0 102 51 51 0 0 132.2
PALMER2C 1.461e-002 1.0e-007 0.0e+000 1250 8 0 0 0 2502 1251 1251 0 0 359.6
PALMER3C 1.954e-002 1.0e-007 0.0e+000 2797 8 0 0 0 5596 2798 2798 0 0 406.3
PALMER4C 5.032e-002 1.0e-007 0.0e+000 2166 8 0 0 0 4334 2167 2167 0 0 382.8
PALMER5C 2.128e+000 1.0e-007 0.0e+000 24 6 0 0 0 50 25 25 0 0 87.8
PALMER6C 1.639e-002 1.0e-007 0.0e+000 2348 8 0 0 0 4698 2349 2349 0 0 388.6
PALMER7C 6.041e-001 1.0e-007 0.0e+000 3060 8 0 0 0 6122 3061 3061 0 0 401.6
PALMER8C 1.598e-001 1.0e-007 0.0e+000 1442 8 0 0 0 2886 1443 1443 0 0 359.7
PARKCH -1.506e+007 1.0e-007 0.0e+000 24 15 0 0 0 35 10 10 0 0 6195.0
ROSENBR 5.204e-022 1.0e-007 0.0e+000 45 2 0 0 0 81 36 36 0 0 84.7
S308 7.732e-001 1.0e-007 0.0e+000 16 2 0 0 0 33 17 17 0 0 82.0
SINEVAL 1.155e-018 1.0e-007 0.0e+000 115 2 0 0 0 220 105 105 0 0 84.2
SISSER 3.751e-011 1.0e-007 0.0e+000 22 2 0 0 0 38 16 16 0 0 83.5
SNAIL 2.402e-022 1.0e-007 0.0e+000 154 2 0 0 0 277 123 123 0 0 91.3
STRATEC -2.578e+007 1.0e-007 0.0e+000 20 10 0 0 0 28 7 7 0 0 1769.0
TOINTGOR 1.374e+003 1.0e-007 0.0e+000 27 50 0 0 0 54 26 26 0 0 151.2
TOINTPSP 2.256e+002 1.0e-007 0.0e+000 74 50 0 0 0 139 64 64 0 0 157.9
TOINTQOR 1.175e+003 1.0e-007 0.0e+000 18 50 0 0 0 38 19 19 0 0 95.2
VIBRBEAM 1.745e-001 1.0e-007 0.0e+000 221 8 0 0 0 443 222 222 0 0 231.5
YFITU 6.670e-013 1.0e-007 0.0e+000 308 3 0 0 0 609 301 301 0 0 121.4
ZANGWIL2 -1.820e+001 1.0e-007 0.0e+000 1 2 0 0 0 3 2 2 0 0 89.4