Results for Moré/Garbow/Hillstrom test problems

unconstrained, using function values only

with the MATLAB Optimization Toolbox

adapted from original source (A. Kuntsevich)

There are two tables, one for the BFGS method, the other for the DFP method


Results obtained by FMINU (BFGS method)
without user-supplied gradients

Test
No.
Function Name
(Dimension)
Function Value At
Solution Found
Known
Minimum
Function
Evaluations
1 Rosenbrock (2) 1.15227e-013 0.00000e+000 150
2 Freudenstein and Roth (2) 4.89843e+001 4.89843e+001 46
3 Powell Badly Scaled (2) 2.72370e-005 0.00000e+000 10001
4 Brown Badly Scaled (2) 2.30447e-005 0.00000e+000 10003
5 Beale (2) 8.96584e-011 0.00000e+000 81
6 Jennrich and Sampson (2) --- 1.24362e+002 Loop
7 Helical Valley (3) 5.14090e-010 0.00000e+000 164
8 Bard (3) 8.21488e-003 8.21487e-003 397
9 Gaussian (3) 1.12793e-008 1.12793e-008 31
10 Meyer (3) 3.46975e+007 8.79458e+001 10002
11 Gulf Research and Dvlp.(3) 9.29169e-007* 0.00000e+000 10004
12 Box 3-Dimensional (3) 8.64446e-010 0.00000e+000 10004
13 Powell Singular (4) 3.92897e-009 0.00000e+000 3415
14 Wood (4) 7.67340e-011 0.00000e+000 515
15 Kowalik and Osborne (4) 3.07506e-004 3.07506e-004 217
16 Brown and Dennis (4) 8.58222e+004 8.58222e+004 110
17 Osborne 1 (5) 5.01191e-002 0.00000e+000 1476
18 Biggs EXP6 (6) 5.65567e-003 5.65565e-003 10003
19 Osborne 2 (11) --- 4.01377e-002 Loop
20 Watson (9) 3.70740e-005 1.39976e-006 5286
21 Extended Rosenbrock (10) 3.30227e-005 0.00000e+000 10006
22 Extended Powell Singular(10) 3.92897e-009 0.00000e+000 3415
23 Penalty I (4) 2.33786e-005 2.24998e-005 10002
24 Penalty II (4) 9.51700e-006 9.37629e-006 74
25 Variably Dimensioned (10) 1.09313e-012 0.00000e+000 2227
26 Trigonometric (10) 2.79506e-005 2.79506e-005 368
28 Discrete Boundary Value (10) 1.47713e-008 0.00000e+000 696
29 Discrete Integral Equat. (10) 8.18057e-012 0.00000e+000 90
30 Broyden Tridiagonal (10) 7.27665e-012 0.00000e+000 224
31 Broyden Banded (10) 2.17652e-011 0.00000e+000 229
32 Linear --- Full Rank (10) 1.00000e+001 1.00000e+001 25
33 Linear --- Rank 1 (10) --- 4.63415e+000 Loop
34 Linear --- Rank 1 with Zero
Columns and Rows (10)
6.13514e+000 6.13514e+000 87

* The coordinates of the solution are far from the minimizer


Results obtained by FMINU (DFP method)
without user-supplied gradients

Test
No.
Function Name
(Dimension)
Function Value At
Solution Found
Known
Minimum
Function
Evaluations
1 Rosenbrock (2) 7.59529e-014 0.00000e+000 178
2 Freudenstein and Roth (2) 4.89843e+001 4.89843e+001 46
3 Powell Badly Scaled (2) 1.55866e-005 0.00000e+000 10001
4 Brown Badly Scaled (2) 1.92892e-005 0.00000e+000 10003
5 Beale (2) 2.86991e-012 0.00000e+000 84
6 Jennrich and Sampson (2) --- 1.24362e+002 Loop
7 Helical Valley (3) 4.08483e-012 0.00000e+000 181
8 Bard (3) 8.21488e-003 8.21487e-003 139
9 Gaussian (3) 1.12794e-008 1.12793e-008 25
10 Meyer (3) --- 8.79458e+001 Loop
11 Gulf Research and Dvlp.(3) --- 0.00000e+000 Loop
12 Box 3-Dimensional (3) 1.42092e-003 0.00000e+000 191
13 Powell Singular (4) --- 0.00000e+000 Loop
14 Wood (4) 2.01217e-001 0.00000e+000 1107
15 Kowalik and Osborne (4) 3.07510e-004 3.07506e-004 10002
16 Brown and Dennis (4) 8.58222e+004 8.58222e+004 109
17 Osborne 1 (5) 6.05020e-005 5.46489e-005 321
18 Biggs EXP6 (6) 4.47386e-004 0.00000e+000 10002
19 Osborne 2 (11) 4.01610e-002 4.01377e-002 10007
20 Watson (9) 5.80443e-005 1.39976e-006 2144
21 Extended Rosenbrock (10) 3.43086e-005 0.00000e+000 1912
22 Extended Powell Singular(10) --- 0.00000e+000 Loop
23 Penalty I (4) 2.40708e-005 2.24998e-005 130
24 Penalty II (4) 9.51698e-006 9.37629e-006 96
25 Variably Dimensioned (10) 2.31323e-011 0.00000e+000 10004
26 Trigonometric (10) 2.79506e-005 2.79506e-005 332
28 Discrete Boundary Value (10) 1.27341e-009 0.00000e+000 10007
29 Discrete Integral Equat. (10) 1.22273e-011 0.00000e+000 90
30 Broyden Tridiagonal (10) 1.35488e-011 0.00000e+000 225
31 Broyden Banded (10) 2.33635e-012 0.00000e+000 228
32 Linear --- Full Rank (10) 1.00000e+001 1.00000e+001 25
33 Linear --- Rank 1 (10) 4.63415e+000 4.63415e+000 10011
34 Linear --- Rank 1 with Zero
Columns and Rows (10)
--- 6.13514e+000 Loop