adapted from original source (A. Kuntsevich)
There are two tables, one with results using function values only, and the other with results using function values and gradients.
| Function Name (Dimension) |
Known minimum |
Function value at the solution |
Function evaluations |
|---|---|---|---|
| Rosenbrock (2) | 0.00000e+000 | 7.38198e-015 | 328 |
| Freudenstein and Roth (2) | 4.89843e+001 | 4.89843e+001 | 203 |
| Powell Badly Scaled (2) | 0.00000e+000 | 4.08410e-017 | 1427 |
| Brown Badly Scaled (2) | 0.00000e+000 | 1.66235e-009 | 663 |
| Beale (2) | 0.00000e+000 | 9.94948e-016 | 120 |
| Jennrich and Sampson (2) | 1.24362e+002 | 1.24362e+002 | 150 |
| Helical Valley (3) | 0.00000e+000 | 6.96029e-017 | 288 |
| Bard (3) | 8.21487e-003 | 8.21488e-003 | 283 |
| Gaussian (3) | 1.12793e-008 | 1.12793e-008 | 254 |
| Meyer (3) | 8.79458e+001 | 8.79459e+001 | 4130 |
| Gulf Research and Dvlp. (3) | 0.00000e+000 | 3.43064e-016 | 2259 |
| Box 3-Dimensional (3) | 0.00000e+000 | 3.98704e-016 | 224 |
| Powell Singular (4) | 0.00000e+000 | 5.36831e-016 | 333 |
| Wood (4) | 0.00000e+000 | 1.10222e-016 | 304 |
| Kowalik and Osborne (4) | 3.07506e-004 | 3.07506e-004 | 432 |
| Brown and Dennis (4) | 8.58222e+004 | 8.58222e+004 | 434 |
| Osborne 1 (5) | 5.46489e-005 | 5.46489e-005 | 949 |
| Biggs EXP6 (6)* | 0.00000e+000 | 4.05880e-015 | 969 |
| Osborne 2 (11) | 4.01377e-002 | 4.01377e-002 | 1320 |
| Watson (9) | 1.39976e-006 | 1.39979e-006 | 1614 |
| Extended Rosenbrock (10) | 0.00000e+000 | 5.46731e-015 | 1846 |
| Extended Powell Singular (4) | 0.00000e+000 | 5.36831e-016 | 333 |
| Penalty I (4) | 2.24998e-005 | 2.24998e-005 | 670 |
| Penalty II (4) | 9.37629e-006 | 9.37629e-006 | 1452 |
| Variably Dimensioned (10) | 0.00000e+000 | 4.63456e-015 | 290 |
| Trigonometric (10) | 2.79506e-005 | 2.79506e-005 | 930 |
| Discrete Boundary Value (10) | 0.00000e+000 | 1.66351e-015 | 623 |
| Discrete Integral Equat. (10) | 0.00000e+000 | 3.32263e-015 | 437 |
| Broyden Tridiagonal (10) | 0.00000e+000 | 6.11193e-015 | 461 |
| Broyden Banded (10) | 0.00000e+000 | 9.26590e-015 | 460 |
| Linear -- Full Rank (10) | 1.00000e+001 | 1.00000e+001 | 988 |
| Linear -- Rank 1 (10) | 4.63415e+000 | 4.63415e+000 | 1136 |
| Linear -- Rank 1 with Zero Columns and Rows (10) | 6.13514e+000 | 6.13514e+000 | 584 |
* - Function no.18 (Biggs) has two minima with function values 0 resp. 0.00565565 (see Table 1).
| Function Name (Dimension) |
Known minimum |
Function value at the solution |
Function evaluations |
Gradient evaluations |
|---|---|---|---|---|
| Rosenbrock (2) | 0.00000e+000 | 7.45326e-018 | 186 | 32 |
| Freudenstein and Roth (2) | 4.89843e+001 | 4.89843e+001 | 133 | 35 |
| Powell Badly Scaled (2) | 0.00000e+000 | 1.74622e-019 | 1067 | 152 |
| Brown Badly Scaled (2) | 0.00000e+000 | 3.30705e-015 | 273 | 39 |
| Beale (2) | 0.00000e+000 | 4.90121e-015 | 82 | 14 |
| Jennrich and Sampson (2) | 1.24362e+002 | 1.24362e+002 | 81 | 27 |
| Helical Valley (3) | 0.00000e+000 | 4.97565e-017 | 192 | 34 |
| Bard (3) | 8.21487e-003 | 8.21488e-003 | 123 | 33 |
| Gaussian (3) | 1.12793e-008 | 1.12793e-008 | 135 | 30 |
| Meyer (3) | 8.79458e+001 | 8.79459e+001 | 2610 | 437 |
| Gulf Research and Dvlp. (3) | 0.00000e+000 | 3.64345e-017 | 1302 | 237 |
| Box 3-Dimensional (3) | 0.00000e+000 | 6.63806e-015 | 143 | 23 |
| Powell Singular (4) | 0.00000e+000 | 1.06277e-015 | 183 | 34 |
| Wood (4) | 0.00000e+000 | 3.43512e-015 | 177 | 34 |
| Kowalik and Osborne (4) | 3.07506e-004 | 3.07506e-004 | 194 | 57 |
| Brown and Dennis (4) | 8.58222e+004 | 8.58222e+004 | 205 | 59 |
| Osborne 1 (5) | 5.46489e-005 | 5.46489e-005 | 371 | 98 |
| Biggs EXP6 (6) | 5.65565e-003 | 5.65565e-003 | 242 | 68 |
| Osborne 2 (11) | 4.01377e-002 | 4.01377e-002 | 293 | 92 |
| Watson (9) | 1.39976e-006 | 1.39976e-006 | 379 | 112 |
| Watson (12) | 4.72238e-010 | 4.72238e-010 | 585 | 168 |
| Extended Rosenbrock (10) | 0.00000e+000 | 5.02975e-015 | 571 | 130 |
| Extended Powell Singular (4) | 0.00000e+000 | 1.06277e-015 | 183 | 34 |
| Penalty I (4) | 2.24998e-005 | 2.24998e-005 | 384 | 87 |
| Penalty II (4) | 9.37629e-006 | 9.37629e-006 | 730 | 178 |
| Penalty II (10) | 2.93660e-004 | 2.93660e-004 | 1076 | 299 |
| Variably Dimensioned (10) | 0.00000e+000 | 2.23875e-015 | 75 | 7 |
| Trigonometric (10) | 2.79506e-005 | 2.79506e-005 | 214 | 71 |
| Discrete Boundary Value (10) | 0.00000e+000 | 4.11813e-015 | 195 | 41 |
| Discrete Integral Equat. (10) | 0.00000e+000 | 9.40681e-015 | 143 | 28 |
| Broyden Tridiagonal (10) | 0.00000e+000 | 6.90182e-015 | 152 | 31 |
| Broyden Banded (10) | 0.00000e+000 | 3.13279e-015 | 154 | 32 |
| Linear -- Full Rank (10) | 1.00000e+001 | 1.00000e+001 | 318 | 99 |
| Linear -- Rank 1 (10) | 4.63415e+000 | 4.63415e+000 | 92 | 19 |
| Linear -- Rank 1 with Zero Columns and Rows (10) | 6.13514e+000 | 6.13514e+000 | 78 | 13 |