Table 2c. The solution for UNC-problems by SolvOpt
without 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
Rosenbrock (2) 0.00000e+000 2.27949e-016 2.79754e-008 942
Freudenstein and Roth (2) 0.00000e+000 1.00156e-015 3.58997e-009 200
Powell Badly Scaled (2) 0.00000e+000 1.00200e-0082 9.90898e-001 185
Brown Badly Scaled (2) 0.00000e+000 3.03840e-013 4.14421e-013 362
Beale (2) 0.00000e+000 1.91982e-014 1.24021e-007 1133
Jennrich and Sampson (2) 1.24362e+002 1.24362e+0023 1.78112e-005 245
Helical Valley (3) 0.00000e+000 8.76344e-015 9.59776e-009 343
Bard (3) 1.74287e+001 1.74287e+001 1.00001e+000 570
Gaussian (3) 4.05102e-001 4.05102e-001 2.07212e-005 135
Meyer (3) 8.79458e+001 8.79459e+001 1.15474e-006 4601
Gulf Research and Dvlp. (3) 0.00000e+000 3.85445e-0154 1.02767e-006 1421
Box 3-Dimensional (3) 0.00000e+000 4.69171e-017 0.00000e+000 174
Powell Singular (4) 0.00000e+000 1.00903e-013 1.66616e-004 412
Wood (4) 0.00000e+000 2.49364e-014 4.06774e-008 789
Kowalik and Osborne (4) 1.79454e-003 1.79460e-003 0.00000e+000 1483
Brown and Dennis (4) 8.58222e+004 8.58222e+004 1.08605e-004 333
Osborne 1 (5) 5.46489e-005 7.96452e-005 9.49943e-001 1526
Biggs EXP6 (6) 5.65565e-003 1.24665e-002 1.00008e+000 1514
Osborne 2 (11) 2.63057e+001 2.63057e+001 0.00000e+000 249
Watson (9) 1.39976e-006 1.39977e-0065 3.43343e-003 1055
Extended Rosenbrock (10) 0.00000e+000 9.00532e-014 2.50035e-007 7859
Extended Powell Singular (4) 0.00000e+000 1.00903e-013 1.66616e-004 412
Penalty I (4) 2.24998e-005 2.24998e-005 6.82586e-005 1383
Penalty II (4) 9.37629e-006 9.37629e-006 4.66152e-005 7918
Variably Dimensioned (10) 0.00000e+000 3.67939e-014 1.28731e-007 1006
Trigonometric (10) 2.79506e-005 4.21864e-005 0.00000e+000 569
Discrete Boundary Value (10) 0.00000e+000 8.24201e-014 5.88519e-006 894
Discrete Integral Equat. (10) 0.00000e+000 2.31018e-013 3.49668e-006 1029
Broyden Tridiagonal (10) 1.36026e+000 1.36026e+000 6.80769e-005 625
Broyden Banded (10) 3.05728e+000 3.05728e+000 7.16243e-005 783
Linear -- Full Rank (10) 1.00000e+001 1.00000e+001 3.63295e-005 1629
Linear -- Rank 1 (10) 4.63415e+000 4.63415e+000 0.00000e+000 785
Linear -- Rank 1 with Zero
Columns and Rows (10) 		6.13514e+000 6.13514e+000 0.00000e+000 773
- 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 1000-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 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.

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