Table 2b. The solution for UNC-problems by SolvOpt
without user-supplied analytically determined gradients
and 100-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
Rosenbrock (2) 0.00000e+000 1.31787e-014 4.46546e-008 733
Freudenstein and Roth (2) 4.89843e+001 4.89843e+001 2.46440e-004 159
Powell Badly Scaled (2) 0.00000e+000 1.01987e-0082 9.09964e-001 664
Brown Badly Scaled (2) 0.00000e+000 6.18511e-013 7.84989e-013 384
Beale (2) 0.00000e+000 1.02889e-014 1.29579e-007 445
Jennrich and Sampson (2) 2.59580e+002 2.59580e+0023 1.20007e-006 138
Helical Valley (3) 0.00000e+000 6.99915e-015 5.54568e-008 250
Bard (3) 8.21487e-003 8.21488e-003 1.03268e-005 308
Gaussian (3) 1.12793e-008 1.12793e-008 1.90031e-005 266
Meyer (3) 8.79458e+001 8.79459e+001 6.77947e-005 6569
Gulf Research and Dvlp. (3) 3.85000e-002 3.85000e-0024 0.00000e+000 150
Box 3-Dimensional (3) 0.00000e+000 2.31450e-024 7.00071e-005 807
Powell Singular (4) 0.00000e+000 1.16607e-013 1.86451e-004 424
Wood (4) 0.00000e+000 1.16243e-014 6.51326e-008 773
Kowalik and Osborne (4) 1.79454e-003 1.79455e-003 0.00000e+000 651
Brown and Dennis (4) 8.58222e+004 8.58222e+004 3.82771e-005 266
Osborne 1 (5) 5.46489e-005 4.76527e-002 1.00000e+000 2380
Biggs EXP6 (6) 3.06367e-001 3.06367e-001 2.46123e-005 472
Osborne 2 (11) 1.78981e+000 1.78981e+000 2.99333e-005 439
Watson (9) 1.39976e-006 1.39977e-0065 3.43343e-003 1055
Extended Rosenbrock (10) 0.00000e+000 1.91484e-013 3.29764e-007 4928
Extended Powell Singular (4) 0.00000e+000 1.16607e-013 1.86451e-004 424
Penalty I (4) 2.24998e-005 2.24998e-005 4.92902e-005 1771
Penalty II (4) 9.37629e-006 9.37629e-006 1.75021e-005 3920
Variably Dimensioned (10) 0.00000e+000 2.62889e-013 3.38158e-007 938
Trigonometric (10) 0.00000e+000 8.66716e-014 0.00000e+000 644
Discrete Boundary Value (10) 0.00000e+000 1.10572e-013 4.58755e-006 785
Discrete Integral Equat. (10) 0.00000e+000 7.84698e-014 3.78180e-006 569
Broyden Tridiagonal (10) 1.02865e+000 1.02865e+000 2.87985e-005 827
Broyden Banded (10) 3.05728e+000 3.05728e+000 2.67913e-005 738
Linear -- Full Rank (10) 1.00000e+001 1.00000e+001 2.14003e-003 604
Linear -- Rank 1 (10) 4.63415e+000 4.63415e+000 0.00000e+000 740
Linear -- Rank 1 with Zero
Columns and Rows (10) 		6.13514e+000 6.13514e+000 0.00000e+000 1190
- Click on the icon to get a detailed explanation.
1 - The nearest known local minimum to the obtained one.
2 - SolvOpt returned the code -14 at the first run. The true minimum was obtained with the next re-start from the obtained point.
3 - A 100-fold random starting point was used for function #6 (Jennrich and Sampson). Reason: function equals infinity at the 100-fold standard starting point.
4 - A 100-fold random starting point was used for function #11 (Gulf Research and Development). Reason: gradient is zero at the 100-fold standard starting point.
5 - A 100-fold random starting point was used for function #20 (Watson), because the standard starting point is the origin.

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