Linearly-constrained OptimizationLast 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 linearly-constrained general optimization benchmark problems.

  • Method choice: Linear search - Discrete Newton
  • Max number of iterations:25000
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.)
AVION2 9.468e+007 1.0e-008 1.0e-010 1 49 49 15 0 153 153 0 1 1 116.2
EQC -8.295e+002 1.0e-008 1.0e-010 11 9 9 3 0 104 104 0 1 1 82.5
EXPFITA 1.137e-003 1.0e-008 1.0e-010 20 5 0 22 0 132 132 0 1 1 79.9
EXPFITB 5.019e-003 1.0e-008 1.0e-010 52 5 0 102 0 235 235 0 1 1 86.5
EXPFITC 2.330e-002 1.0e-008 1.0e-010 235 5 0 502 0 869 869 0 1 1 226.5
HIMMELBI -1.736e+003 1.0e-008 1.0e-010 276 100 100 12 0 22031 22031 0 1 1 534.6
HIMMELBJ -1.910e+003 1.0e-005 1.0e-010 157 45 45 14 0 5625 5625 0 1 1 361.9
HONG 2.257e+001 1.0e-008 1.0e-010 5 4 4 1 0 35 35 0 1 1 75.6
HS105 1.062e+003 1.0e-008 1.0e-010 20 8 8 1 0 188 188 0 1 1 166.8
HS112 -4.776e+001 1.0e-008 1.0e-010 6 10 10 3 0 88 88 0 1 1 80.1
HS119 2.449e+002 1.0e-008 1.0e-010 65 16 16 8 0 543 543 0 1 1 120.7
HS24 -1.000e+000 1.0e-008 1.0e-010 3 2 2 3 0 17 17 0 1 1 76.6
HS36 -3.300e+003 1.0e-008 1.0e-010 3 3 3 1 0 19 19 0 1 1 75.8
HS37 -3.456e+003 1.0e-008 1.0e-010 5 3 3 2 0 29 29 0 1 1 79.5
HS41 1.926e+000 1.0e-008 1.0e-010 5 4 4 1 0 23 23 0 1 1 76.0
HS49 6.962e-009 1.0e-008 1.0e-010 15 5 0 2 0 111 111 0 1 1 78.2
HS50 6.384e-013 1.0e-008 1.0e-010 8 5 0 3 0 62 62 0 1 1 90.3
HS54 -9.005e-001 1.0e-005 1.0e-010 15519 6 6 1 0 124159 124159 0 1 1 715.5
HS55 6.667e+000 1.0e-008 1.0e-010 0 6 6 6 0 7 7 0 1 1 77.0
HS62 -2.627e+004 1.0e-008 1.0e-010 6 3 3 1 0 35 35 0 1 1 75.6
HS86 -3.235e+001 1.0e-008 1.0e-010 14 5 5 10 0 78 78 0 1 1 78.7
HS9 -5.000e-001 1.0e-008 1.0e-010 1 2 0 1 0 7 7 0 1 1 74.1
HUBFIT 1.689e-002 1.0e-008 1.0e-010 4 2 1 1 0 15 15 0 1 1 76.1
HYDROELS -3.582e+006 1.0e-005 1.0e-010 20183 169 169 168 0 3395040 3395040 0 1 1 46110.0
LIN -4.651e-011 1.0e-008 1.0e-010 2 4 4 2 0 14 14 0 1 1 78.9
LOADBAL 4.529e-001 1.0e-008 1.0e-010 93 31 31 31 0 2770 2770 0 1 1 295.2
ODFITS -2.380e+003 1.0e-008 1.0e-010 4 10 10 6 0 59 59 0 1 1 114.7
PENTAGON 1.462e-004 1.0e-008 1.0e-010 7 6 0 15 0 55 55 0 1 1 91.3
QC -9.565e+002 1.0e-008 1.0e-010 7 9 9 4 0 71 71 0 1 1 87.3
QCNEW -8.065e+002 1.0e-008 1.0e-010 11 9 9 3 0 104 104 0 1 1 84.0
STANCMIN 4.250e+000 1.0e-008 1.0e-010 5 3 3 2 0 4 4 0 1 1 77.1
TFI3 4.301e+000 1.0e-008 1.0e-010 22 3 0 101 0 64 64 0 1 1 83.2

CUTE linearly-constrained general optimization benchmark problems.

  • Method choice: Linear search - Newton
  • Max number of iterations:25000
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.)
AVION2 9.468e+007 1.0e-008 1.0e-010 2 49 49 15 0 89 89 3 1 1 95.9
EQC -8.295e+002 1.0e-008 1.0e-010 11 9 9 3 0 83 83 3 1 1 119.6
EXPFITA 1.137e-003 1.0e-008 1.0e-010 20 5 0 22 0 42 42 18 1 1 77.6
EXPFITB 5.019e-003 1.0e-008 1.0e-010 52 5 0 102 0 75 75 32 1 1 88.1
EXPFITC 2.330e-002 1.0e-008 1.0e-010 235 5 0 502 0 254 254 123 1 1 239.6
HIMMELBI -1.736e+003 1.0e-008 1.0e-010 276 100 100 12 0 431 431 216 1 1 389.4
HIMMELBJ -1.908e+003 1.0e-005 1.0e-010 73 45 45 14 0 446 446 34 1 1 187.7
HONG 2.257e+001 1.0e-008 1.0e-010 5 4 4 1 0 11 11 6 1 1 77.6
HS105 1.062e+003 1.0e-008 1.0e-010 20 8 8 1 0 54 54 17 1 1 144.9
HS112 -4.776e+001 1.0e-008 1.0e-010 6 10 10 3 0 18 18 7 1 1 76.5
HS119 2.449e+002 1.0e-008 1.0e-010 65 16 16 8 0 63 63 30 1 1 93.3
HS24 -1.000e+000 1.0e-008 1.0e-010 3 2 2 3 0 9 9 4 1 1 77.7
HS36 -3.300e+003 1.0e-008 1.0e-010 3 3 3 1 0 7 7 4 1 1 80.8
HS37 -3.456e+003 1.0e-008 1.0e-010 5 3 3 2 0 11 11 6 1 1 85.2
HS41 1.926e+000 1.0e-008 1.0e-010 5 4 4 1 0 7 7 4 1 1 88.9
HS49 6.962e-009 1.0e-008 1.0e-010 15 5 0 2 0 31 31 16 1 1 81.9
HS50 6.384e-013 1.0e-008 1.0e-010 8 5 0 3 0 17 17 9 1 1 77.9
HS54 -9.005e-001 1.0e-005 1.0e-010 15519 6 6 1 0 31039 31039 15520 1 1 581.2
HS55 6.667e+000 1.0e-008 1.0e-010 0 6 6 6 0 1 1 1 1 1 90.0
HS62 -2.627e+004 1.0e-008 1.0e-010 6 3 3 1 0 14 14 7 1 1 84.6
HS86 -3.235e+001 1.0e-008 1.0e-010 14 5 5 10 0 23 23 11 1 1 100.0
HS9 -5.000e-001 1.0e-008 1.0e-010 1 2 0 1 0 3 3 2 1 1 78.5
HUBFIT 1.689e-002 1.0e-008 1.0e-010 4 2 1 1 0 7 7 4 1 1 97.7
HYDROELS -3.582e+006 1.0e-005 1.0e-010 20183 169 169 168 0 40177 40177 20089 1 1 16060.0
LIN -4.651e-011 1.0e-008 1.0e-010 2 4 4 2 0 11 11 1 1 1 83.4
LOADBAL 4.529e-001 1.0e-008 1.0e-010 93 31 31 31 0 166 166 84 1 1 138.6
ODFITS -2.380e+003 1.0e-008 1.0e-010 4 10 10 6 0 9 9 5 1 1 83.2
PENTAGON 1.462e-004 1.0e-008 1.0e-010 7 6 0 15 0 13 13 7 1 1 79.5
QC -9.565e+002 1.0e-008 1.0e-010 7 9 9 4 0 15 15 8 1 1 88.0
QCNEW -8.065e+002 1.0e-008 1.0e-010 11 9 9 3 0 83 83 3 1 1 105.1
STANCMIN 4.250e+000 1.0e-008 1.0e-010 5 3 3 2 0 1 1 1 1 1 79.1
TFI3 4.301e+000 1.0e-008 1.0e-010 22 3 0 101 0 25 25 13 1 1 83.5

CUTE linearly-constrained general optimization benchmark problems.

  • Method choice: Linear search - Quasi Newton
  • Max number of iterations:25000
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.)
AVION2 9.468e+007 1.0e-008 1.0e-010 7 49 49 15 0 55 55 0 1 1 108.0
EQC -8.295e+002 1.0e-008 1.0e-010 11 9 9 3 0 74 74 0 1 1 318.6
EXPFITA 1.137e-003 1.0e-008 1.0e-010 25 5 0 22 0 86 86 0 1 1 314.6
EXPFITB 5.019e-003 1.0e-008 1.0e-010 56 5 0 102 0 112 112 0 1 1 87.0
EXPFITC 2.330e-002 1.0e-008 1.0e-010 237 5 0 502 0 262 262 0 1 1 146.6
HIMMELBI -1.736e+003 1.0e-008 1.0e-010 453 100 100 12 0 1395 1395 0 1 1 354.5
HIMMELBJ -1.896e+003 1.0e-005 1.0e-010 80 45 45 14 0 1362 1362 0 1 1 214.3
HONG 2.257e+001 1.0e-008 1.0e-010 7 4 4 1 0 29 29 0 1 1 78.4
HS105 1.062e+003 1.0e-008 1.0e-010 39 8 8 1 0 94 94 0 1 1 119.5
HS112 -4.776e+001 1.0e-008 1.0e-010 19 10 10 3 0 92 92 0 1 1 81.4
HS119 2.449e+002 1.0e-008 1.0e-010 83 16 16 8 0 106 106 0 1 1 95.5
HS24 -1.000e+000 1.0e-008 1.0e-010 12 2 2 3 0 27 27 0 1 1 72.9
HS36 -3.300e+003 1.0e-008 1.0e-010 3 3 3 1 0 8 8 0 1 1 73.8
HS37 -3.456e+003 1.0e-008 1.0e-010 8 3 3 2 0 18 18 0 1 1 83.3
HS41 1.926e+000 1.0e-008 1.0e-010 7 4 4 1 0 11 11 0 1 1 74.1
HS49 6.976e-009 1.0e-008 1.0e-010 22 5 0 2 0 48 48 0 1 1 79.5
HS50 6.897e-012 1.0e-008 1.0e-010 10 5 0 3 0 24 24 0 1 1 75.0
HS54 -1.560e-001 1.0e-005 1.0e-010 7 6 6 1 0 56 56 0 1 1 81.1
HS55 6.667e+000 1.0e-008 1.0e-010 0 6 6 6 0 1 1 0 1 1 74.5
HS62 -2.627e+004 1.0e-008 1.0e-010 9 3 3 1 0 38 38 0 1 1 92.1
HS86 -3.235e+001 1.0e-008 1.0e-010 16 5 5 10 0 31 31 0 1 1 81.0
HS9 -5.000e-001 1.0e-008 1.0e-010 3 2 0 1 0 48 48 0 1 1 70.9
HUBFIT 1.689e-002 1.0e-008 1.0e-010 5 2 1 1 0 10 10 0 1 1 79.2
HYDROELS -3.582e+006 1.0e-005 1.0e-010 20278 169 169 168 0 44072 44072 0 1 1 4811.0
LIN -2.020e-002 1.0e-008 1.0e-010 16 4 4 2 0 125 125 0 1 1 94.0
LOADBAL 4.529e-001 1.0e-008 1.0e-010 100 31 31 31 0 298 298 0 1 1 122.5
ODFITS -2.380e+003 1.0e-008 1.0e-010 34 10 10 6 0 108 108 0 1 1 89.6
PENTAGON 1.508e-004 1.0e-008 1.0e-010 11 6 0 15 0 60 60 0 1 1 79.9
QC -9.565e+002 1.0e-008 1.0e-010 7 9 9 4 0 283 283 0 1 1 95.2
QCNEW -8.065e+002 1.0e-008 1.0e-010 11 9 9 3 0 19 19 0 1 1 74.3
STANCMIN 4.250e+000 1.0e-008 1.0e-010 5 3 3 2 0 1 1 0 1 1 74.1
TFI3 4.301e+000 1.0e-008 1.0e-010 22 3 0 101 0 25 25 0 1 1 81.8