Table 6. The solution for UNC-problems at
f=10-8f0
by SolvOpt
without 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 |
|---|
| Rosenbrock (2) | 0.00000e+000 | 2.45975e-018 | 1.45405e-005 | 220 |
| Freudenstein and Roth (2) | 4.89843e-007 | 4.89843e-007 | 2.79035e-004 | 130 |
| Powell Badly Scaled (2) | 0.00000e+000 | 5.24568e-018 | 2.07736e-002 | 1013 |
| Brown Badly Scaled (2) | 0.00000e+000 | 1.39069e-013 | 2.75470e-009 | 221 |
| Beale (2) | 0.00000e+000 | 5.62156e-020 | 7.39267e-007 | 142 |
| Jennrich and Sampson (2) | 1.24362e-006 | 1.24362e-006 | 4.20676e-006 | 331 |
| Helical Valley (3) | 0.00000e+000 | 3.71261e-017 | 5.91828e-006 | 209 |
| Bard (3) | 8.21487e-011 | 8.21488e-011 | 2.96598e-005 | 164 |
| Gaussian (3) | 1.12793e-016 | 1.12811e-016 | 1.92546e-005 | 72 |
| Meyer (3) | 8.79458e-007 | 8.79459e-007 | 1.87496e-005 | 4718 |
| Gulf Research and Dvlp. (3) | 0.00000e+000 | 9.37700e-018 | 4.31605e-002 | 1998 |
| Box 3-Dimensional (3) | 0.00000e+000 | 2.17987e-019 | 1.29138e-005 | 154 |
| Powell Singular (4) | 0.00000e+000 | 2.23496e-020 | 4.80161e-004 | 300 |
| Wood (4) | 0.00000e+000 | 5.99588e-020 | 2.35093e-006 | 405 |
| Kowalik and Osborne (4) | 3.07506e-012 | 3.07506e-012 | 1.11486e-005 | 257 |
| Brown and Dennis (4) | 8.58222e-004 | 8.58222e-004 | 1.52573e-005 | 270 |
| Osborne 1 (5) | 5.46489e-013 | 5.46490e-013 | 1.69799e-004 | 840 |
| Biggs EXP6 (6) | 0.00000e+000 | 2.09737e-020 | 7.50011e-001 | 1006 |
| Osborne 2 (11) | 4.01377e-010 | 4.01377e-010 | 1.64311e-005 | 975 |
| Watson (9) | 1.39976e-014 | 1.39976e-014 | 1.12250e-003 | 1078 |
| Extended Rosenbrock (10) | 0.00000e+000 | 8.42101e-019 | 1.17798e-005 | 1929 |
| Extended Powell Singular (4) | 0.00000e+000 | 2.23496e-020 | 4.80161e-004 | 300 |
| Penalty I (4) | 2.24998e-013 | 2.24998e-013 | 6.73601e-005 | 709 |
| Penalty II (4) | 9.37629e-014 | 9.37629e-014 | 1.47015e-005 | 2052 |
| Variably Dimensioned (10) | 0.00000e+000 | 2.14165e-017 | 2.30403e-005 | 187 |
| Trigonometric (10) | 2.79506e-013 | 2.79506e-013 | 0.00000e+000 | 445 |
| Discrete Boundary Value (10) | 0.00000e+000 | 6.93565e-020 | 2.71857e-005 | 524 |
| Discrete Integral Equat. (10) | 0.00000e+000 | 4.75741e-020 | 2.29617e-005 | 364 |
| Broyden Tridiagonal (10) | 0.00000e+000 | 1.19652e-016 | 2.69216e-005 | 267 |
| Broyden Banded (10) | 2.68022e-008 | 2.68022e-008 | 1.00402e-005 | 1107 |
| Linear -- Full Rank (10) | 1.00000e-007 | 1.00000e-007 | 2.71211e-005 | 293 |
| Linear -- Rank 1 (10) | 4.63415e-008 | 4.63415e-008 | 0.00000e+000 | 1747 |
Linear -- Rank 1 with Zero
Columns and Rows (10) | 6.13514e-008 | 6.13514e-008 | 0.00000e+000 | 1336 |
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