Results for Moré et al. problems

using SolvOpt, Shor's minimization method with space dilation (in Fortran, C and Matlab, by Alexei Kuntsevich and Franz Kappel)

adapted from original source (A. Kuntsevich)

There are two tables, one with results using function values only, and the other with results using function values and gradients.


Results without user-supplied gradients

Function Name
(Dimension)
Known
minimum
Function value
at the solution
Function
evaluations
Rosenbrock (2) 0.00000e+000 7.38198e-015 328
Freudenstein and Roth (2) 4.89843e+001 4.89843e+001 203
Powell Badly Scaled (2) 0.00000e+000 4.08410e-017 1427
Brown Badly Scaled (2) 0.00000e+000 1.66235e-009 663
Beale (2) 0.00000e+000 9.94948e-016 120
Jennrich and Sampson (2) 1.24362e+002 1.24362e+002 150
Helical Valley (3) 0.00000e+000 6.96029e-017 288
Bard (3) 8.21487e-003 8.21488e-003 283
Gaussian (3) 1.12793e-008 1.12793e-008 254
Meyer (3) 8.79458e+001 8.79459e+001 4130
Gulf Research and Dvlp. (3) 0.00000e+000 3.43064e-016 2259
Box 3-Dimensional (3) 0.00000e+000 3.98704e-016 224
Powell Singular (4) 0.00000e+000 5.36831e-016 333
Wood (4) 0.00000e+000 1.10222e-016 304
Kowalik and Osborne (4) 3.07506e-004 3.07506e-004 432
Brown and Dennis (4) 8.58222e+004 8.58222e+004 434
Osborne 1 (5) 5.46489e-005 5.46489e-005 949
Biggs EXP6 (6)* 0.00000e+000 4.05880e-015 969
Osborne 2 (11) 4.01377e-002 4.01377e-002 1320
Watson (9) 1.39976e-006 1.39979e-006 1614
Extended Rosenbrock (10) 0.00000e+000 5.46731e-015 1846
Extended Powell Singular (4) 0.00000e+000 5.36831e-016 333
Penalty I (4) 2.24998e-005 2.24998e-005 670
Penalty II (4) 9.37629e-006 9.37629e-006 1452
Variably Dimensioned (10) 0.00000e+000 4.63456e-015 290
Trigonometric (10) 2.79506e-005 2.79506e-005 930
Discrete Boundary Value (10) 0.00000e+000 1.66351e-015 623
Discrete Integral Equat. (10) 0.00000e+000 3.32263e-015 437
Broyden Tridiagonal (10) 0.00000e+000 6.11193e-015 461
Broyden Banded (10) 0.00000e+000 9.26590e-015 460
Linear -- Full Rank (10) 1.00000e+001 1.00000e+001 988
Linear -- Rank 1 (10) 4.63415e+000 4.63415e+000 1136
Linear -- Rank 1 with Zero
Columns and Rows (10)
6.13514e+000 6.13514e+000 584

* - Function no.18 (Biggs) has two minima with function values 0 resp. 0.00565565 (see Table 1).


Results with user-supplied gradients

Function Name
(Dimension)
Known
minimum
Function value
at the solution
Function
evaluations
Gradient
evaluations
Rosenbrock (2) 0.00000e+000 7.45326e-018 186 32
Freudenstein and Roth (2) 4.89843e+001 4.89843e+001 133 35
Powell Badly Scaled (2) 0.00000e+000 1.74622e-019 1067 152
Brown Badly Scaled (2) 0.00000e+000 3.30705e-015 273 39
Beale (2) 0.00000e+000 4.90121e-015 82 14
Jennrich and Sampson (2) 1.24362e+002 1.24362e+002 81 27
Helical Valley (3) 0.00000e+000 4.97565e-017 192 34
Bard (3) 8.21487e-003 8.21488e-003 123 33
Gaussian (3) 1.12793e-008 1.12793e-008 135 30
Meyer (3) 8.79458e+001 8.79459e+001 2610 437
Gulf Research and Dvlp. (3) 0.00000e+000 3.64345e-017 1302 237
Box 3-Dimensional (3) 0.00000e+000 6.63806e-015 143 23
Powell Singular (4) 0.00000e+000 1.06277e-015 183 34
Wood (4) 0.00000e+000 3.43512e-015 177 34
Kowalik and Osborne (4) 3.07506e-004 3.07506e-004 194 57
Brown and Dennis (4) 8.58222e+004 8.58222e+004 205 59
Osborne 1 (5) 5.46489e-005 5.46489e-005 371 98
Biggs EXP6 (6) 5.65565e-003 5.65565e-003 242 68
Osborne 2 (11) 4.01377e-002 4.01377e-002 293 92
Watson (9) 1.39976e-006 1.39976e-006 379 112
Watson (12) 4.72238e-010 4.72238e-010 585 168
Extended Rosenbrock (10) 0.00000e+000 5.02975e-015 571 130
Extended Powell Singular (4) 0.00000e+000 1.06277e-015 183 34
Penalty I (4) 2.24998e-005 2.24998e-005 384 87
Penalty II (4) 9.37629e-006 9.37629e-006 730 178
Penalty II (10) 2.93660e-004 2.93660e-004 1076 299
Variably Dimensioned (10) 0.00000e+000 2.23875e-015 75 7
Trigonometric (10) 2.79506e-005 2.79506e-005 214 71
Discrete Boundary Value (10) 0.00000e+000 4.11813e-015 195 41
Discrete Integral Equat. (10) 0.00000e+000 9.40681e-015 143 28
Broyden Tridiagonal (10) 0.00000e+000 6.90182e-015 152 31
Broyden Banded (10) 0.00000e+000 3.13279e-015 154 32
Linear -- Full Rank (10) 1.00000e+001 1.00000e+001 318 99
Linear -- Rank 1 (10) 4.63415e+000 4.63415e+000 92 19
Linear -- Rank 1 with Zero
Columns and Rows (10)
6.13514e+000 6.13514e+000 78 13


Global Optimization Test Results
Optimization Test Problem Collection
Global Optimization