Table 1c. The solution for UNC-problems by SolvOpt
with user-supplied analytically determined gradients
and 1000-fold 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 1.16588e-015 5.51745e-008 531 106
Freudenstein and Roth (2) 0.00000e+000 3.30550e-014 5.88948e-009 137 21
Powell Badly Scaled (2) 0.00000e+000 1.00200e-0082 9.90896e-001 107 19
Brown Badly Scaled (2) 0.00000e+000 6.05869e-015 6.69537e-014 269 56
Beale (2) 0.00000e+000 5.28568e-016 2.99064e-008 431 81
Jennrich and Sampson (2) 2.59580e+002 2.59580e+0023 1.19302e-006 91 16
Helical Valley (3) 0.00000e+000 3.83003e-013 7.53435e-008 164 36
Bard (3) 1.74287e+001 1.74287e+001 0.00000e+000 1329 200
Gaussian (3) 4.05102e-001 4.05102e-001 3.13199e-005 84 15
Meyer (3) 8.79458e+001 8.79459e+001 5.46902e-006 4873 1092
Gulf Research and Dvlp. (3) 0.00000e+000 4.35062e-0164 1.28804e-005 250 57
Box 3-Dimensional (3) 0.00000e+000 6.51289e-019 0.00000e-000 120 14
Powell Singular (4) 0.00000e+000 1.76150e-013 1.82260e-004 205 48
Wood (4) 0.00000e+000 3.20014e-014 4.25849e-008 403 97
Kowalik and Osborne (4) 1.79454e-003 1.79454e-003 0.00000e+000 435 90
Brown and Dennis (4) 8.58222e+004 8.58222e+004 6.05448e-005 189 57
Osborne 1 (5) 5.46489e-005 5.46489e-005 1.78972e-004 1726 452
Biggs EXP6 (6) 5.65565e-003 5.65565e-003 1.82710e-005 1332 329
Osborne 2 (11) 2.63057e+001 2.63057e+001 0.00000e+000 136 27
Watson (9) 1.39976e-006 1.39976e-0065 1.81276e-005 304 97
Extended Rosenbrock (10) 0.00000e+000 3.22159e-013 5.28219e-007 2584 720
Extended Powell Singular (4) 0.00000e+000 1.76150e-013 1.82260e-004 205 48
Penalty I (4) 2.24998e-005 2.24998e-005 4.74024e-005 163 36
Penalty II (4) 9.37629e-006 9.37629e-006 1.11843e-005 2776 717
Variably Dimensioned (10) 0.00000e+000 1.02211e-013 1.65603e-007 429 82
Trigonometric (10) 2.79506e-005 2.79506e-005 0.00000e+000 166 55
Discrete Boundary Value (10) 0.00000e+000 3.47725e-013 4.53260e-006 250 64
Discrete Integral Equat. (10) 0.00000e+000 5.29115e-013 4.33152e-006 281 71
Broyden Tridiagonal (10) 1.36026e+000 1.36026e+000 2.55023e-005 188 54
Broyden Banded (10) 3.05728e+000 3.05728e+000 9.84502e-005 219 66
Linear -- Full Rank (10) 1.00000e+001 1.00000e+001 6.14377e-005 441 119
Linear -- Rank 1 (10) 4.63415e+000 4.63415e+000 0.00000e+000 206 37
Linear -- Rank 1 with Zero
Columns and Rows (10)		 6.13514e+000 6.13514e+000 0.00000e+000 266 24
- Click on the icon to get a detailed explanation.
1 - The nearest known local minimum to the obtained one.
2 - SolvOpt return code is -14: Result is inaccurate in function values. The function is extremely steep.
True minimum was obtained with the next re-start from the obtained point.
3 - A 1000-fold random starting point was used for function #6 (Jennrich and Sampson). Reason: function equals infinity at the 1000-fold standard starting point.
4 - A 1000-fold random starting point was used for function #11 (Gulf Research and Development). Reason: gradient is zero at the 1000-fold standard starting point.
5 - A 1000-fold random starting point was used for function #20 (Watson), because the standard starting point is the origin.

  Previous table: Table 1b   Back to the Results   Next table: Table 2