Theory and Modern Applications
From: On q-BFGS algorithm for unconstrained optimization problems
k | \(q^{k}\) | \(x=(2, 3)^{T}\) | |||
---|---|---|---|---|---|
f(x) | \(f(q^{k}x)\) | \(g_{q^{k}}(1)\) | \(g_{q^{k}}(2)\) | ||
1 | \((0.3200, 0.3200)^{T}\) | 8.4877 | 7.3482 | 4.0387 | 0.5585 |
2 | \((0.9200, 0.9200)^{T}\) | 8.4877 | 8.4043 | 6.8282 | 0.3474 |
3 | \((0.9060, 0.9060)^{T}\) | 8.4877 | 8.3889 | 6.7358 | 0.3501 |
4 | \((0.9535, 0.9535)^{T}\) | 8.4877 | 8.4401 | 7.0561 | 0.3413 |
5 | \((0.9669, 0.9669)^{T}\) | 8.4877 | 8.4540 | 7.1500 | 0.3390 |
6 | \((0.9765, 0.9765)^{T}\) | 8.4877 | 8.4639 | 7.2183 | 0.3373 |
7 | \((0.9823, 0.9823)^{T}\) | 8.4877 | 8.4698 | 7.2598 | 0.3363 |
8 | \((0.9862, 0.9862)^{T}\) | 8.4877 | 8.4738 | 7.2881 | 0.3357 |
9 | \((0.9890, 0.9890)^{T}\) | 8.4877 | 8.4766 | 7.3080 | 0.3352 |
10 | \((0.9910, 0.9910)^{T} \) | 8.4877 | 8.4786 | 7.3226 | 0.3349 |
11 | \((0.9925, 0.9925)^{T}\) | 8.4877 | 8.4801 | 7.3336 | 0.3346 |
12 | \((0.9936, 0.9936)^{T}\) | 8.4877 | 8.4813 | 7.3420 | 0.3344 |
13 | \((0.9945, 0.9945)^{T}\) | 8.4877 | 8.4822 | 7.3487 | 0.3343 |
14 | \((0.9952, 0.9952)^{T}\) | 8.4877 | 8.4829 | 7.3541 | 0.3341 |
15 | \((0.9958, 0.9958)^{T}\) | 8.4877 | 8.4835 | 7.3584 | 0.3340 |
16 | \((0.9963, 0.9963)^{T}\) | 8.4877 | 8.4840 | 7.3620 | 0.3339 |
17 | \((0.9967, 0.9967)^{T}\) | 8.4877 | 8.4844 | 7.3650 | 0.3339 |
18 | \((0.9971, 0.9971)^{T}\) | 8.4877 | 8.4847 | 7.3675 | 0.3338 |
19 | \((0.9974, 0.9974)^{T}\) | 8.4877 | 8.4850 | 7.3697 | 0.3338 |
20 | \((0.9976, 0.9976)^{T}\) | 8.4877 | 8.4853 | 7.3715 | 0.3337 |
21 | \((0.9978, 0.9978)^{T}\) | 8.4877 | 8.4855 | 7.3731 | 0.3337 |
22 | \((0.9980, 0.9980)^{T}\) | 8.4877 | 8.4857 | 7.3745 | 0.3337 |
23 | \((0.9982, 0.9982)^{T}\) | 8.4877 | 8.4859 | 7.3757 | 0.3336 |
24 | \((0.9983, 0.9983)^{T}\) | 8.4877 | 8.4860 | 7.3768 | 0.3336 |
25 | \((0.9985, 0.9985)^{T}\) | 8.4877 | 8.4861 | 7.3777 | 0.3336 |
26 | \((0.9986, 0.9986)^{T}\) | 8.4877 | 8.4862 | 7.3785 | 0.3336 |
27 | \((0.9987, 0.9987)^{T}\) | 8.4877 | 8.4863 | 7.3793 | 0.3336 |
28 | \((0.9988, 0.9988)^{T}\) | 8.4877 | 8.4864 | 7.3800 | 0.3335 |
29 | \((0.9989, 0.9989)^{T}\) | 8.4877 | 8.4865 | 7.3806 | 0.3335 |
30 | \((0.9989, 0.9989)^{T}\) | 8.4877 | 8.4866 | 7.3811 | 0.3335 |