Table 1b. The solution for UNC-problems by SolvOpt
with 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 Gradient evaluations
Rosenbrock (2) 0.00000e+000 1.46014e-015 5.93008e-008 430 81
Freudenstein and Roth (2) 4.89843e+001 4.89843e+001 2.54827e-004 119 33
Powell Badly Scaled (2) 0.00000e+000 1.01957e-00829.11347e-001 910 172
Brown Badly Scaled (2) 0.00000e+000 3.66675e-013 5.97493e-013 241 49
Beale (2) 0.00000e+000 7.18655e-014 5.92833e-008 323 61
Jennrich and Sampson (2) 2.59580e+002 2.59580e+00233.76410e-006 94 17
Helical Valley (3) 0.00000e+000 3.84520e-014 7.69103e-009 152 30
Bard (3) 8.21487e-003 8.21488e-003 2.12543e-005 173 40
Gaussian (3) 1.12793e-008 1.12793e-008 1.91498e-005 214 51
Meyer (3) 8.79458e+001 8.79459e+001 1.24427e-006 2116 483
Gulf Research and Dvlp. (3) 3.85000e-002 3.85000e-00240.00000e+000 98 36
Box 3-Dimensional (3) 0.00000e+000 1.62931e-014 4.23037e-007 296 62
Powell Singular (4) 0.00000e+000 3.98985e-013 3.59994e-004 173 40
Wood (4) 0.00000e+000 2.31324e-014 2.29879e-008 445 106
Kowalik and Osborne (4) 1.79454e-003 1.79454e-003 0.00000e+000 446 99
Brown and Dennis (4) 8.58222e+004 8.58222e+004 4.58495e-006 172 53
Osborne 1 (5) 5.46489e-005 5.46489e-005 1.71956e-004 1064 278
Biggs EXP6 (6) 3.06367e-001 3.06367e-001 1.84660e-005 295 46
Osborne 2 (11) 1.78981e+000 1.78981e+000 3.63038e-005 205 43
Watson (9) 1.39976e-006 1.39976e-00651.81276e-005 304 97
Extended Rosenbrock (10) 0.00000e+000 6.64418e-014 3.20008e-007 955 254
Extended Powell Singular (4) 0.00000e+000 3.98985e-013 3.59994e-004 173 40
Penalty I (4) 2.24998e-005 2.24998e-005 5.70390e-005 351 87
Penalty II (4) 9.37629e-006 9.37629e-006 1.64129e-005 3519 907
Variably Dimensioned (10) 0.00000e+000 6.25838e-013 4.75498e-007 273 52
Trigonometric (10) 2.79506e-005 2.79506e-005 0.00000e+000 190 53
Discrete Boundary Value (10) 0.00000e+000 6.34348e-014 5.33083e-006 234 55
Discrete Integral Equat. (10) 0.00000e+000 2.15657e-013 3.72913e-006 162 32
Broyden Tridiagonal (10) 1.02865e+000 1.02865e+000 4.29951e-005 236 66
Broyden Banded (10) 3.05728e+000 3.05728e+000 7.83767e-005 223 66
Linear -- Full Rank (10) 1.00000e+001 1.00000e+001 5.78263e-005 409 117
Linear -- Rank 1 (10) 4.63415e+000 4.63415e+000 0.00000e+000 203 38
Linear -- Rank 1 with Zero
Columns and Rows (10)
6.13514e+000 6.13514e+000 0.00000e+000 367 37
- 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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