Table 1. The solution for UNC-problems (set of tests by Moré et al.)
by SolvOpt with user-supplied
analytically determined gradients
and standard starting points
| 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 |
Gradient evaluations |
|---|
| Rosenbrock (2) | 0.00000e+000 | 6.51487e-014 | 4.57175e-007 | 177 | 38 |
| Freudenstein and Roth (2) | 4.89843e+001 | 4.89843e+001 | 2.19319e-004 | 92 | 27 |
| Powell Badly Scaled (2) | 0.00000e+000 | 4.15387e-013 | 5.77221e-004 | 754 | 149 |
| Brown Badly Scaled (2) | 0.00000e+000 | 2.81555e-015 | 4.66825e-014 | 222 | 37 |
| Beale (2) | 0.00000e+000 | 9.73165e-016 | 3.29049e-008 | 94 | 20 |
| Jennrich and Sampson (2) | 1.24362e+002 | 1.24362e+002 | 1.88848e-005 | 56 | 20 |
| Helical Valley (3) | 0.00000e+000 | 2.67613e-014 | 4.12264e-008 | 153 | 36 |
| Bard (3) | 8.21487e-003 | 8.21488e-003 | 2.95678e-005 | 107 | 33 |
| Gaussian (3) | 1.12793e-008 | 1.12793e-008 | 1.90770e-005 | 71 | 19 |
| Meyer (3) | 8.79458e+001 | 8.79459e+001 | 1.70764e-005 | 2246 | 521 |
| Gulf Research and Dvlp. (3) | 0.00000e+000 | 2.97735e-015 | 1.09601e-005 | 1152 | 258 |
| Box 3-Dimensional (3) | 0.00000e+000 | 4.73124e-013 | 1.32117e-006 | 116 | 23 |
| Powell Singular (4) | 0.00000e+000 | 1.42035e-013 | 2.52338e-004 | 133 | 31 |
| Wood (4) | 0.00000e+000 | 7.05286e-015 | 6.70780e-008 | 248 | 56 |
| Kowalik and Osborne (4) | 3.07506e-004 | 3.07506e-004 | 6.01813e-005 | 108 | 36 |
| Brown and Dennis (4) | 8.58222e+004 | 8.58222e+004 | 2.59210e-005 | 158 | 53 |
| Osborne 1 (5) | 5.46489e-005 | 5.46489e-005 | 1.94239e-004 | 305 | 89 |
| Biggs EXP6 (6) | 5.65565e-003 | 5.65565e-003 | 9.59768e-006 | 141 | 43 |
| Osborne 2 (11) | 4.01377e-002 | 4.01377e-002 | 1.73261e-005 | 216 | 75 |
| Watson (9) | 1.39976e-006 | 1.39976e-006 | 1.81276e-005 | 304 | 97 |
| Extended Rosenbrock (10) | 0.00000e+000 | 1.78220e-013 | 4.75103e-007 | 321 | 81 |
| Extended Powell Singular (4) | 0.00000e+000 | 1.42035e-013 | 2.52338e-004 | 133 | 31 |
| Penalty I (4) | 2.24998e-005 | 2.24998e-005 | 5.60111e-005 | 254 | 67 |
| Penalty II (4) | 9.37629e-006 | 9.37629e-006 | 8.78873e-005 | 986 | 264 |
| Variably Dimensioned (10) | 0.00000e+000 | 2.08035e-013 | 2.51484e-007 | 399 | 86 |
| Trigonometric (10) | 2.79506e-005 | 2.79506e-005 | 0.00000e+000 | 143 | 49 |
| Discrete Boundary Value (10) | 0.00000e+000 | 8.52721e-014 | 4.58385e-006 | 161 | 40 |
| Discrete Integral Equat. (10) | 0.00000e+000 | 6.85021e-013 | 7.15789e-006 | 111 | 27 |
| Broyden Tridiagonal (10) | 0.00000e+000 | 8.91327e-014 | 7.27062e-007 | 119 | 30 |
| Broyden Banded (10) | 0.00000e+000 | 6.75979e-013 | 9.80184e-007 | 141 | 30 |
| Linear -- Full Rank (10) | 1.00000e+001 | 1.00000e+001 | 3.23741e-005 | 379 | 113 |
| Linear -- Rank 1 (10) | 4.63415e+000 | 4.63415e+000 | 0.00000e+000 | 133 | 24 |
Linear -- Rank 1 with Zero
Columns and Rows (10) | 6.13514e+000 | 6.13514e+000 | 0.00000e+000 | 289 | 24 |
Back to the Results
Next table: Table 1a