Theory and Modern Applications
Table 7 Comparison details with [23]
From: On q-BFGS algorithm for unconstrained optimization problems
Problem number | q-BFGS | ||||
|---|---|---|---|---|---|
it | fe | ge | \(x^{*}\) | \(f(x^{*})\) | |
1 | 4 | 29 | 5 | \((-0.062 , -0.036)^{T}\) | 0.000 |
2 | 5 | 33 | 6 | \((5.901 , 0.509)^{T}\) | −42.868 |
3 | 34 | 200 | 40 | \((0.001 , -0.012)^{T}\) | 2.36E − 12 |
4 | 7 | 42 | 9 | \((2.999 , 0.499)^{T}\) | 9.06E − 15 |
5 | 6 | 35 | 7 | \((-0.002 , -0.000)^{T}\) | 2.18e − 06 |
6 | 8 | 60 | 9 | \((0.000 , 0.000)^{T}\) | 6.60e − 07 |
7 | 3 | 21 | 5 | \((-10.2 , -6 , 2.66)^{T}\) | 4.71e − 18 |
8 | 5 | 27 | 6 | \((9.426 , 2.478)^{T}\) | 0.398 |
9 | 7 | 41 | 9 | \((-0.012 , 0.006)^{T}\) | 5.68e − 11 |
10 | 7 | 39 | 9 | \((-0.095 , 0.717)^{T}\) | −1.032 |
11 | 5 | 30 | 6 | \((6.2868 , 0.4000)^{T}\) | −41.835 |
12 | 23 | 137 | 25 | \((1.0 , 1.0 , 1.0 , 1.0)^{T}\) | 2.11e − 16 |
13 | 6 | 32 | 7 | \((3.1417 , 3.1416)^{T}\) | −1 |
14 | 4 | 23 | 5 | \((-1.9686, 16.1968)^{T}\) | 4.16e − 22 |
15 | 9 | 73 | 11 | \((0.0026 , -1.0000)^{T}\) | 3.0006 |
16 | 7 | 44 | 8 | \((0.0002, -0.0143)^{T}\) | 1.08E − 07 |
17 | 9 | 55 | 10 | \((4.976 , 4.858)^{T}\) | −176.542 |
18 | 12 | 98 | 14 | \((0.110 , 0.556 , 0.852)^{T}\) | −3.863 |
19 | 6 | 47 | 9 | \((4.000 , 3.999 , 4.000 , 3.999)^{T}\) | −10.536 |
Problem number | q-BFGS | ||||
|---|---|---|---|---|---|
it | fe | ge | \(x^{*}\) | \(f(x^{*})\) | |
1 | 7 | 44 | 8 | \((2.6\mbox{e}{-}06 , -3.3\mbox{e}{-}06)^{T}\) | 0 |
2 | 3 | 21 | 4 | \((5.506 , 0.507)^{T}\) | −42.868 |
3 | 36 | 202 | 42 | \((0.003 ,-0.016)^{T}\) | 1.3612e − 11 |
4 | 8 | 47 | 10 | \((2.999 , 0.499)^{T}\) | 6.33e − 15 |
5 | 7 | 40 | 8 | \((5.23\mbox{e}{-}05 1.3\mbox{e}{-}06)^{T}\) | 6.46e − 14 |
6 | 9 | 51 | 11 | \((8.9\mbox{e}{-}06 , -1.32\mbox{e}{-}05)^{T}\) | 1.39e − 15 |
7 | 3 | 21 | 5 | \((-10.2 , -6 , 2.66)^{T}\) | 4.36e − 18 |
8 | 6 | 32 | 7 | \((9.425 , 2.475)^{T}\) | 0.398 |
9 | 7 | 41 | 9 | \((-0.011 , 0.006)^{T}\) | 2.66e − 16 |
10 | 8 | 44 | 10 | \((-0.089 , 0.712)^{T}\) | −1.032 |
11 | 5 | 31 | 7 | \((6.2868 , 0.4000)^{T}\) | −41.835 |
12 | 24 | 144 | 26 | \((1.0 , 1.0 , 1.0 1.0)^{T}\) | 6.12e − 14 |
13 | 7 | 36 | 8 | \((3.1441 , 3.1422)^{T}\) | −1 |
14 | 4 | 23 | 5 | \((-1.9690 , 16.1962)^{T}\) | 4.16e − 22 |
15 | 10 | 62 | 13 | \((0.0000 , -1.0000)^{T}\) | 3 |
16 | 8 | 41 | 9 | \((-6.75\mbox{e}{-}05 , 5.4\mbox{e}{-}06)^{T}\) | 0 |
17 | 9 | 56 | 11 | \((4.976 , 4.858)^{T}\) | −176.542 |
18 | 13 | 103 | 15 | \((0.115 ,0.556 ,0.853)^{T}\) | −3.863 |
19 | 6 | 52 | 8 | \((4.000 , 3.999,4.000 , 3.999)^{T}\) | −10.536 |