Table 3. The solution for UNC-problems at f=1016f0 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 4.97968e-014 2.22045e-016 257 55
Freudenstein and Roth (2) 4.89842e+017 4.89843e+017 2.56530e-004 95 28
Powell Badly Scaled (2) 0.00000e+000 2.23100e-014 2.06098e-010 946 177
Brown Badly Scaled (2) 0.00000e+000 4.73810e-013 6.77626e-021 295 53
Beale (2) 0.00000e+000 1.18329e-014 1.33227e-015 194 43
Jennrich and Sampson (2) 1.24362e+018 1.24362e+018 2.29124e-005 72 24
Helical Valley (3) 0.00000e+000 5.29962e-014 1.68874e-015 245 62
Bard (3) 8.21487e+013 8.21488e+013 1.88758e-005 113 34
Gaussian (3) 1.12793e+008 1.12793e+008 1.90960e-005 85 30
Meyer (3) 8.79458e+017 8.79459e+017 2.79887e-005 2227 519
Gulf Research and Dvlp. (3) 0.00000e+000 2.14070e-013 7.79607e-013 1159 274
Box 3-Dimensional (3) 0.00000e+000 8.94248e-014 3.10862e-015 192 47
Powell Singular (4) 0.00000e+000 1.65278e-013 4.14052e-008 207 55
Wood (4) 0.00000e+000 1.02975e-011 1.95399e-014 455 107
Kowalik and Osborne (4) 3.07505e+012 3.07506e+012 1.42948e-005 122 42
Brown and Dennis (4) 8.58222e+020 8.58222e+020 2.59210e-005 158 53
Osborne 1 (5) 5.46489e+011 5.46489e+011 1.89522e-004 311 91
Biggs EXP6 (6) 5.65565e+013 5.65565e+013 1.50906e-005 160 49
Osborne 2 (11) 4.01377e+014 4.01377e+014 2.54674e-005 249 84
Watson (9) 1.39976e+010 1.39976e+010 1.35395e-005 302 97
Extended Rosenbrock (10) 0.00000e+000 7.43008e-013 8.43769e-015 633 169
Extended Powell Singular (4) 0.00000e+000 1.65278e-013 4.14052e-008 207 55
Penalty I (4) 2.24998e+011 2.24998e+011 6.83807e-005 766 197
Penalty II (4) 9.37629e+010 9.37629e+010 2.81388e-005 902 242
Variably Dimensioned (10) 0.00000e+000 1.57439e-012 6.43929e-015 481 122
Trigonometric (10) 2.79506e+011 2.79506e+011 0.00000e+000 133 52
Discrete Boundary Value (10) 0.00000e+000 3.80904e-014 3.00153e-006 258 83
Discrete Integral Equat. (10) 0.00000e+000 2.20311e-013 3.00153e-006 216 66
Broyden Tridiagonal (10) 0.00000e+000 3.62617e-011 7.29343e-007 259 81
Broyden Banded (10) 0.00000e+000 3.58015e-011 8.92225e-007 246 77
Linear -- Full Rank (10) 1.00000e+017 1.00000e+017 6.97892e-005 416 114
Linear -- Rank 1 (10) 4.63415e+016 4.63415e+016 0.00000e+000 129 24
Linear -- Rank 1 with Zero
Columns and Rows (10)
6.13514e+016 6.13514e+016 0.00000e+000 183 38
1 - The nearest known local minimum to the obtained one.

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