Table 1a. The solution for UNC-problems by SolvOpt
with user-supplied analytically determined gradients
and 10-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 0.00000e+000 7.51423e-011 293 56
Freudenstein and Roth (2) 0.00000e+000 0.00000e+000 2.81634e-008 108 12
Powell Badly Scaled (2) 0.00000e+000 0.00000e+000 7.91773e-006 587 105
Brown Badly Scaled (2) 0.00000e+000 0.00000e+000 3.47677e-017 287 54
Beale (2) 0.00000e+000 0.00000e+000 8.69515e-010 110 13
Jennrich and Sampson (2) 2.59580e+002 2.59580e+002 9.52837e-006 145 15
Helical Valley (3) 0.00000e+000 0.00000e+000 2.44155e-008 177 34
Bard (3) 8.21487e-003 8.21487e-003 2.24049e-005 142 37
Gaussian (3) 1.12793e-008 1.12793e-008 1.90641e-005 139 37
Meyer (3) 8.79458e+001 8.79458e+001 1.55588e-006 3064 698
Gulf Research and Dvlp. (3) 0.00000e+000 0.00000e+000 2.32879e-005 570 122
Box 3-Dimensional (3) 0.00000e+000 0.00000e+000 1.31294e-007 149 26
Powell Singular (4) 0.00000e+000 0.00000e+000 1.73320e-004 174 39
Wood (4) 0.00000e+000 0.00000e+000 2.95308e-007 188 44
Kowalik and Osborne (4) 3.07506e-004 3.07506e-004 2.08879e-005 252 75
Brown and Dennis (4) 8.58222e+004 8.58222e+004 1.02400e-005 158 49
Osborne 1 (5) 5.46489e-005 5.46489e-005 1.91065e-004 764 206
Biggs EXP6 (6) 5.65565e-003 5.65565e-003 1.09581e-005 182 51
Osborne 2 (11) 1.78981e+000 1.78981e+000 6.32109e-006 111 31
Watson (9) 1.39976e-006 1.39976e-00621.81276e-005 304 97
Extended Rosenbrock (10) 0.00000e+000 0.00000e+000 2.28135e-007 581 150
Extended Powell Singular (4) 0.00000e+000 0.00000e+000 1.73320e-004 174 39
Penalty I (4) 2.24998e-005 2.24998e-005 3.91451e-005 993 246
Penalty II (4) 9.37629e-006 9.37629e-006 6.68322e-005 2322 598
Variably Dimensioned (10) 0.00000e+000 0.00000e+000 3.50943e-007 150 27
Trigonometric (10) 2.79506e-005 2.79506e-005 0.00000e+000 152 45
Discrete Boundary Value (10) 0.00000e+000 0.00000e+000 5.36053e-006 183 45
Discrete Integral Equat. (10) 0.00000e+000 0.00000e+000 7.68693e-006 136 30
Broyden Tridiagonal (10) 1.02865e+000 1.02865e+000 3.57473e-005 178 52
Broyden Banded (10) 3.05728e+000 3.05728e+000 1.30099e-004 183 57
Linear -- Full Rank (10) 1.00000e+001 1.00000e+001 1.41431e-005 376 109
Linear -- Rank 1 (10) 4.63415e+000 4.63415e+000 0.00000e+000 143 24
Linear -- Rank 1 with Zero
Columns and Rows (10)		 6.13514e+000 6.13514e+000 0.00000e+000 255 23
- Click on the icon to get a detailed explanation.
2 - A 10-fold random starting point was used for function #20 (Watson), because the standard starting point is the origin.

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