without user-supplied analytically determined gradients
and 10-fold standard starting points
maxi ( |xo,i-x*,i| / | x*,i| )
Columns and Rows (10)
| Function Name (Dimension) | Known minimum1: f(xo) | Function value at the obtained solution: f(x*) | Relative error for the point: maxi ( |xo,i-x*,i| / | x*,i| ) |
Function evaluations |
|---|---|---|---|---|
| Rosenbrock (2) | 0.00000e+000 | 7.58087e-014 | 3.44446e-007 | 391 |
| Freudenstein and Roth (2) | 0.00000e+000 | 8.62925e-019 | 1.30916e-010 | 157 |
| Powell Badly Scaled (2) | 0.00000e+000 | 2.06387e-014 | 1.29900e-004 | 813 |
| Brown Badly Scaled (2) | 0.00000e+000 | 5.39722e-013 | 6.64848e-013 | 372 |
| Beale (2) | 0.00000e+000 | 1.77368e-014 | 1.25467e-007 | 113 |
| Jennrich and Sampson (2) | 2.59580e+002 | 2.59580e+002 | 6.52618e-006 | 189 |
| Helical Valley (3) | 0.00000e+000 | 1.58442e-014 | 1.21589e-008 | 309 |
| Bard (3) | 8.21487e-003 | 8.21488e-003 | 1.81347e-005 | 220 |
| Gaussian (3) | 1.12793e-008 | 1.12793e-008 | 1.90685e-005 | 177 |
| Meyer (3) | 8.79458e+001 | 8.79459e+001 | 9.12535e-006 | 5639 |
| Gulf Research and Dvlp. (3) | 0.00000e+000 | 2.48354e-029 | 3.83693e-015 | 56 |
| Box 3-Dimensional (3) | 0.00000e+000 | 8.26211e-016 | 2.89864e-007 | 265 |
| Powell Singular (4) | 0.00000e+000 | 1.70074e-014 | 1.05084e-004 | 363 |
| Wood (4) | 0.00000e+000 | 5.48393e-013 | 3.00902e-007 | 509 |
| Kowalik and Osborne (4) | 3.07506e-004 | 3.07506e-004 | 1.60094e-005 | 525 |
| Brown and Dennis (4) | 8.58222e+004 | 8.58222e+004 | 5.84471e-005 | 302 |
| Osborne 1 (5) | 5.46489e-005 | 5.46489e-005 | 1.86884e-004 | 1939 |
| Biggs EXP6 (6) | 0.00000e+000 | 6.57960e-014 | 3.48933e-006 | 1511 |
| Osborne 2 (11) | 1.78981e+000 | 1.78981e+000 | 6.98157e-006 | 403 |
| Watson (9) | 1.39976e-006 | 1.39977e-006 | 3.43343e-003 | 1055 |
| Extended Rosenbrock (10) | 0.00000e+000 | 1.97271e-014 | 1.44637e-007 | 2255 |
| Extended Powell Singular (4) | 0.00000e+000 | 1.70074e-014 | 1.05084e-004 | 363 |
| Penalty I (4) | 2.24998e-005 | 2.24998e-005 | 3.57181e-005 | 2199 |
| Penalty II (4) | 9.37629e-006 | 9.37629e-006 | 3.93628e-005 | 6479 |
| Variably Dimensioned (10) | 0.00000e+000 | 1.39395e-014 | 7.32350e-008 | 476 |
| Trigonometric (10) | 0.00000e+000 | 2.17149e-013 | 0.00000e+000 | 514 |
| Discrete Boundary Value (10) | 0.00000e+000 | 2.01974e-013 | 9.38823e-006 | 644 |
| Discrete Integral Equat. (10) | 0.00000e+000 | 2.69188e-013 | 4.35960e-006 | 402 |
| Broyden Tridiagonal (10) | 1.02865e+000 | 1.02865e+000 | 8.75151e-005 | 553 |
| Broyden Banded (10) | 3.05728e+000 | 3.05728e+000 | 9.42520e-005 | 561 |
| Linear -- Full Rank (10) | 1.00000e+001 | 1.00000e+001 | 3.38445e-005 | 347 |
| Linear -- Rank 1 (10) | 4.63415e+000 | 4.63415e+000 | 0.00000e+000 | 872 |
| Linear -- Rank 1 with Zero Columns and Rows (10) | 6.13514e+000 | 6.13514e+000 | 0.00000e+000 | 941 |
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