Nonlinear ProgrammingLast 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 non-linear programming benchmark problems.

  • Method choice: SQP
  • Max number of iterations:7000
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.)
ALLINITA 3.419e+001 1.0e-008 1.0e-010 0 4 3 2 2 1 1 0 1 1 81.8
ALLINITC 2.187e+001 1.0e-008 1.0e-010 6 4 3 0 1 16 16 0 16 16 205.8
ALSOTAME 1.147e-012 1.0e-008 1.0e-010 41 2 2 0 1 88 88 0 88 88 283.2
BATCH 1.443e-012 1.0e-008 1.0e-010 54 48 48 72 1 109 109 0 1 2 357.7
BRITGAS -8.630e+000 1.0e-008 1.0e-010 8 450 450 0 360 101 101 0 0 101 2093.0
BT11 8.249e-001 1.0e-008 1.0e-010 11 5 0 1 2 25 25 0 1 17 83.1
BT6 2.770e-001 1.0e-008 1.0e-010 17 5 0 0 2 38 38 0 0 38 115.5
CRESC100 7.752e-001 1.0e-008 1.0e-010 2 6 4 0 200 119 119 0 0 119 304.7
CRESC4 -1.309e+004 1.0e-008 1.0e-010 33 6 4 0 8 145 145 0 0 145 127.0
CRESC50 2.861e+000 1.0e-008 1.0e-010 5 6 4 0 100 26 26 0 0 26 138.7
DIPIGRI 6.806e+002 1.0e-008 1.0e-010 14 7 0 0 4 38 38 0 0 38 87.4
HS100 6.806e+002 1.0e-008 1.0e-010 14 7 0 0 4 38 38 0 0 38 84.3
HS100LNP 6.806e+002 1.0e-008 1.0e-010 17 7 0 0 2 49 49 0 0 49 92.5
HS100MOD 6.787e+002 1.0e-008 1.0e-010 14 7 0 0 4 39 39 0 0 39 54.8
HS101 1.810e+003 1.0e-008 1.0e-010 45 7 7 0 5 153 153 0 0 153 141.9
HS102 9.119e+002 1.0e-008 1.0e-010 36 7 7 0 5 118 118 0 0 118 140.1
HS103 5.437e+002 1.0e-008 1.0e-010 76 7 7 0 5 219 219 0 0 219 163.8
HS104 3.951e+000 1.0e-008 1.0e-010 18 8 8 0 5 40 40 0 0 40 89.2
HS107 1.434e+030 1.0e-008 1.0e-010 3 9 5 0 6 25 25 0 0 25 83.4
HS109 0.000e+000 1.0e-008 1.0e-010 0 9 9 2 8 1 1 0 1 1 81.4
HS111 -4.776e+001 1.0e-008 1.0e-010 59 10 10 0 3 139 139 0 0 139 142.6
HS111LNP -4.776e+001 1.0e-008 1.0e-010 59 10 0 0 3 139 139 0 0 139 140.2
HS26 1.014e-012 1.0e-008 1.0e-010 25 3 0 0 1 51 51 0 0 51 90.2
HS40 -2.500e-001 1.0e-008 1.0e-010 5 4 0 0 3 12 12 0 0 12 78.0
HS46 6.816e-013 1.0e-008 1.0e-010 32 5 0 0 2 66 66 0 0 66 109.8
HS47 5.227e-013 1.0e-008 1.0e-010 25 5 0 0 3 57 57 0 0 57 86.8
HS56 -3.456e+000 1.0e-008 1.0e-010 11 7 0 0 4 25 25 0 0 25 68.7
HS60 3.257e-002 1.0e-008 1.0e-010 7 3 3 0 1 16 16 0 0 16 80.9
HS64 -1.028e+015 1.0e-008 1.0e-010 4 3 3 0 1 98 98 0 0 98 86.4
HS67 -1.206e+003 1.0e-008 1.0e-010 25 3 3 0 14 93 93 0 0 93 105.1
HS68 6.356e-017 1.0e-008 1.0e-010 10 4 4 0 2 72 72 0 0 72 111.1
HS69 -2.298e+013 1.0e-008 1.0e-010 2 4 4 0 2 78 78 0 0 78 93.4
HS7 -1.732e+000 1.0e-008 1.0e-010 16 2 0 0 1 46 46 0 0 46 102.1
HS71 1.685e+001 1.0e-008 1.0e-010 8 4 4 0 2 18 18 0 0 18 78.4
HS74 5.126e+003 1.0e-008 1.0e-010 9 4 4 2 3 23 23 0 1 14 84.8
HS75 5.174e+003 1.0e-008 1.0e-010 8 4 4 2 3 21 21 0 1 13 85.6
HS77 2.415e-001 1.0e-008 1.0e-010 15 5 0 0 2 34 34 0 0 34 91.9
HS78 -2.920e+000 1.0e-008 1.0e-010 8 5 0 0 3 20 20 0 0 20 96.0
HS79 7.878e-002 1.0e-008 1.0e-010 10 5 0 0 3 22 22 0 0 22 53.6
HS80 5.395e-002 1.0e-008 1.0e-010 6 5 5 0 3 13 13 0 0 13 118.3
HS81 5.395e-002 1.0e-008 1.0e-010 9 5 5 0 3 23 23 0 0 23 102.9
HS85 -2.221e+000 1.0e-008 1.0e-010 25 5 5 1 20 73 73 0 1 70 123.6
HS87 8.995e+003 1.0e-008 1.0e-010 4 6 6 0 4 83 83 0 0 83 107.8
HS93 1.351e+002 1.0e-008 1.0e-010 11 6 6 0 2 24 24 0 0 24 114.6
HS99 -7.764e+008 1.0e-008 1.0e-010 0 7 7 0 2 26 26 0 0 26 94.8
HS99EXP -1.255e+012 1.0e-008 1.0e-010 3154 31 10 0 21 6835 6835 0 0 6835 1037.0
LAUNCH 2.300e-001 1.0e-006 1.0e-010 119 25 25 18 10 610 610 0 1 218 340.5
MESH -3.409e+005 1.0e-008 1.0e-010 137 41 39 28 20 434 434 0 1 181 380.5
NET1 0.000e+000 1.0e-008 1.0e-010 8 48 28 37 20 21 21 0 1 8 132.6
NET2 3.410e+002 1.0e-008 1.0e-010 65 144 79 96 64 322 322 0 1 129 710.8
NET3 1.672e+003 1.0e-008 1.0e-010 79 464 244 305 216 564 564 0 1 234 11550.0
READING6 -1.815e+002 1.0e-008 1.0e-010 3028 102 52 0 50 6225 6225 0 0 6225 10060.0
SYNTHES1 -9.310e+008 1.0e-003 1.0e-010 6 6 6 4 2 21 21 0 1 8 86.7
SYNTHES2 -1.114e+001 1.0e-008 1.0e-010 16 11 11 11 3 42 42 0 1 10 90.1
SYNTHES3 1.183e+001 1.0e-008 1.0e-010 17 17 17 19 4 41 41 0 1 8 106.1
TWOBARS 1.509e+000 1.0e-008 1.0e-010 9 2 2 0 2 26 26 0 0 26 83.6
ZAMB2-8 -7.276e-001 1.0e-008 1.0e-010 887 138 138 0 48 1779 1779 0 0 1779 3800.0
ZAMB2-9 -7.273e-001 1.0e-008 1.0e-010 922 138 138 0 48 1848 1848 0 0 1848 3959.0
ZAMB2-10 -5.347e+046 1.0e-004 1.0e-010 57 270 270 0 96 500 500 0 0 500 3758.0
ZAMB2-11 -1.025e+048 1.0e-008 1.0e-010 48 270 270 0 96 221 221 0 0 221 3470.0

COPS non-linear programming benchmark problems.

  • Method choice: SQP
  • Max number of iterations:1000
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.)
Max-Polygon -7.840e-001 1.0e-006 3.0e-010 167 98 98 48 1176 349 348 0 410424 409248 1040.0
Sphere-Electron 1.055e+003 1.0e-006 1.1e-010 335 150 0 0 50 926 925 0 46300 46250 1990.0