Results for Moré/Garbow/Hillstrom test problems

unconstrained, using function values and gradients

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)
with user-supplied gradients

Test
No.
Function Name
(Dimension)
Function Value At
Solution Found
Known
Minimum
Function
Evaluations
Gradient
Evaluations
1 Rosenbrock (2) 3.84961e-018 0.00000e+000 89 27
2 Freudenstein and Roth (2) 4.89843e+001 4.89843e+001 22 7
3 Powell Badly Scaled (2) 9.45298e-025 0.00000e+000 389 118
4 Brown Badly Scaled (2) 1.97215e-031 0.00000e+000 45 10
5 Beale (2) 4.95393e-023 0.00000e+000 37 12
6 Jennrich and Sampson (2) --- 1.24362e+002 Loop Loop
7 Helical Valley (3) 6.71023e-016 0.00000e+000 70 22
8 Bard (3) 8.21488e-003 8.21487e-003 34 11
9 Gaussian (3) 1.12793e-008 1.12793e-008 9 3
10 Meyer (3) --- 8.79458e+001 Loop Loop
11 Gulf Research and Dvlp.(3) 4.45116e-008* 0.00000e+000 89 26
12 Box 3-Dimensional (3) 5.47254e-021 0.00000e+000 80 25
13 Powell Singular (4) 1.79541e-013 0.00000e+000 89 26
14 Wood (4) 6.84684e-022 0.00000e+000 216 66
15 Kowalik and Osborne (4) 3.07506e-004 3.07506e-004 62 20
16 Brown and Dennis (4) 8.58222e+004 8.58222e+004 50 15
17 Osborne 1 (5) 5.48735e-005 5.46489e-005 76 25
18 Biggs EXP6 (6) 5.65565e-003 5.65565e-003 83 25
19 Osborne 2 (11) 4.01377e-002 4.01377e-002 149 46
20 Watson (9) 1.39976e-006 1.39976e-006 115 34
20' Watson (12) 1.58293e-007 4.72238e-010 96 29
21 Extended Rosenbrock (10) 1.76940e-009 0.00000e+000 220 68
22 Extended Powell Singular(10) 1.79541e-013 0.00000e+000 89 26
23 Penalty I (4) 2.24998e-005 2.24998e-005 127 38
24 Penalty II (4) 9.51699e-006 9.37629e-006 20 6
25 Variably Dimensioned (10) 1.08993e-015 0.00000e+000 27 8
26 Trigonometric (10) 2.79506e-005 2.79506e-005 66 21
28 Discrete Boundary Value (10) 3.17263e-022 0.00000e+000 41 13
29 Discrete Integral Equat. (10) 6.78021e-015 0.00000e+000 17 6
30 Broyden Tridiagonal (10) 6.52829e-013 0.00000e+000 47 15
31 Broyden Banded (10) 4.22003e-011 0.00000e+000 59 18
32 Linear --- Full Rank (10) 1.00000e+001 1.00000e+001 12 4
33 Linear --- Rank 1 (10) 4.63415e+000 4.63415e+000 5 2
34 Linear --- Rank 1 with Zero
Columns and Rows (10)
6.13514e+000 6.13514e+000 5 2

* The coordinates of the solution are far from the minimizer


Results obtained by FMINU (DFP method)
with user-supplied gradients

Test
No.
Function Name
(Dimension)
Function Value At
Solution Found
Known
Minimum
Function
Evaluations
Gradient
Evaluations
1 Rosenbrock (2) 1.41218e-018 0.00000e+000 101 28
2 Freudenstein and Roth (2) 4.89843e+001 4.89843e+001 22 7
3 Powell Badly Scaled (2) 2.28988e-021 0.00000e+000 375 105
4 Brown Badly Scaled (2) 1.26912e-019 0.00000e+000 27 9
5 Beale (2) 5.54246e-018 0.00000e+000 37 12
6 Jennrich and Sampson (2) --- 1.24362e+002 Loop Loop
7 Helical Valley (3) 2.89712e-017 0.00000e+000 68 20
8 Bard (3) 8.21488e-003 8.21487e-003 40 12
9 Gaussian (3) 1.12793e-008 1.12793e-008 9 3
10 Meyer (3) --- 8.79458e+001 Loop Loop
11 Gulf Research and Dvlp.(3) 4.78571e-023 0.00000e+000 2555 707
12 Box 3-Dimensional (3) 2.47649e-018 0.00000e+000 87 26
13 Powell Singular (4) 1.94050e-016 0.00000e+000 116 34
14 Wood (4) 7.82222e+000 0.00000e+000 85 24
15 Kowalik and Osborne (4) 3.07506e-004 3.07506e-004 90 28
16 Brown and Dennis (4) 8.58222e+004 8.58222e+004 49 15
17 Osborne 1 (5) 5.62505e-005 5.46489e-005 78 24
18 Biggs EXP6 (6) 5.65565e-003 5.65565e-003 142 41
19 Osborne 2 (11) 4.01377e-002 4.01377e-002 167 49
20 Watson (9) 6.68133e-006 1.39976e-006 106 31
21 Extended Rosenbrock (10) 5.89040e-016 0.00000e+000 117 34
22 Extended Powell Singular(10) 1.94050e-016 0.00000e+000 116 34
23 Penalty I (4) 2.40387e-005 2.24998e-005 32 9
24 Penalty II (4) 9.51698e-006 9.37629e-006 20 6
25 Variably Dimensioned (10) 1.15839e-016 0.00000e+000 27 8
26 Trigonometric (10) 2.79506e-005 2.79506e-005 76 23
28 Discrete Boundary Value (10) 1.59569e-021 0.00000e+000 41 13
29 Discrete Integral Equat. (10) 1.13362e-014 0.00000e+000 18 6
30 Broyden Tridiagonal (10) 7.42368e-013 0.00000e+000 48 15
31 Broyden Banded (10) 2.49166e-012 0.00000e+000 65 19
32 Linear --- Full Rank (10) 1.00000e+001 1.00000e+001 12 4
33 Linear --- Rank 1 (10) 4.63415e+000 4.63415e+000 5 2
34 Linear --- Rank 1 with Zero
Columns and Rows (10)
6.13514e+000 6.13514e+000 5 2