Table 2 Numerical results of Example 5.2 using Algorithm 1
From: A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems
Sl. no. | Starting point | q-PRP algorithm | ||||
|---|---|---|---|---|---|---|
Step-length | q-gradient | \(x^{*}\) | \(f(x^{*})\) | NI | ||
1 | \((-4.1448E+00,-2.9324E+00)^{T}\) | 2.3367E − 02 | \((1.4775E+00,-7.0264E-01)^{T}\) | \((1.0415E+00,1.0814E+00)^{T}\) | 2.9218E − 03 | 26 |
2 | \((-4.2752E+00,-2.8376E+00)^{T}\) | 4.3899E − 05 | \((-4.9287E-02,-1.8236E-03)^{T}\) | \((1.0046E+00,1.0093E+00)^{T}\) | 2.1377E − 05 | 23 |
3 | \((3.0101E+00,-5.8300E-02)^{T}\) | 7.9493E − 03 | \((4.7749E-02,-6.2513E-02)^{T}\) | \((9.9178E-01,9.8337E-01)^{T}\) | 7.4429E − 05 | 19 |
4 | \((2.4348E+00,-2.8090E+00)^{T}\) | 2.6283E − 01 | \((8.0440E-01,-4.0639E-01)^{T}\) | \((1.0202E+00,1.0388E+00)^{T}\) | 7.9812E − 04 | 25 |
5 | \((2.4944E+00,8.7790E-01)^{T}\) | 1.8736E − 42 | \((-4.9341E-03,-4.9406E-03)^{T}\) | \((1.0255E+00,1.0517E+00)^{T}\) | 6.5168E − 04 | 18 |
6 | \((2.3033E+00,4.0372E+00)^{T}\) | 1.5548E − 02 | \((3.1725E-03,-1.0430E-03)^{T}\) | \((1.0344E+00,1.0701E+00)^{T}\) | 1.1861E − 03 | 20 |
7 | \((-1.1390E-01,3.9092E+00)^{T}\) | 3.9223E − 37 | \((-4.4790E-02,-9.2646E-04)^{T}\) | \((1.0081E+00,1.0163E+00)^{T}\) | 6.5406E − 05 | 24 |
8 | \((-2.7857E+00,1.0782E+00)^{T}\) | 4.2172E − 38 | \((-7.2107E-03,-1.6834E-02)^{T}\) | \((1.0111E+00,1.0222E+00)^{T}\) | 1.2234E − 04 | 18 |
9 | \((-2.6272E+00,1.9875E+00)^{T}\) | 8.1062E − 01 | \((9.6266E-01,-4.4836E-01)^{T}\) | \((1.0471E+00,1.0941E+00)^{T}\) | 2.6921E − 03 | 16 |
10 | \((-4.1150E-01,-3.0219E+00)^{T}\) | 8.0059E − 39 | \((-2.7351E-02,-9.0127E-03)^{T}\) | \((1.0087E+00,1.0175E+00)^{T}\) | 7.5592E − 05 | 16 |
11 | \((4.6309E+00,-4.6946E+00)^{T}\) | 7.1986E − 04 | \((-2.4447E-02,-3.1051E-02)^{T}\) | \((9.8658E-01,9.7324E-01)^{T}\) | 1.8118E − 04 | 29 |
12 | \((4.6810E-01,2.4407E+00)^{T}\) | 4.3738E − 02 | \((-1.8246E+00,8.8302E-01)^{T}\) | \((1.0756E+00,1.1614E+00)^{T}\) | 7.7209E − 03 | 12 |
13 | \((2.1140E-01,2.0000E-04)^{T}\) | 1.0000E + 00 | \((1.6658E-01,-7.9139E-02)^{T}\) | \((1.0354E+00,1.0717E+00)^{T}\) | 1.2627E − 03 | 19 |
14 | \((-2.6841E+00,-2.0080E-01)^{T}\) | 4.3478E − 37 | \((-3.8200E-02,-8.7571E-03)^{T}\) | \((1.0031E+00,1.0061E+00)^{T}\) | 9.3228E − 06 | 12 |
15 | \((-1.1100E-01,4.0472E+00)^{T}\) | 2.3756E − 03 | \((-1.3487E-02,-2.8364E-02)^{T}\) | \((9.9525E-01,9.9043E-01)^{T}\) | 2.3413E − 05 | 19 |
16 | \((1.2406E+00,1.0987E+00)^{T}\) | 4.4170E − 03 | \((-3.8603E-01,1.9025E-01)^{T}\) | \((1.0391E+00,1.0806E+00)^{T}\) | 1.6267E − 03 | 6 |
17 | \((1.7914E+00,1.1767E+00)^{T}\) | 7.7842E − 42 | \((-1.2518E-02,4.0719E-03)^{T}\) | \((1.0316E+00,1.0643E+00)^{T}\) | 9.9856E − 04 | 13 |
18 | \((-1.0448E+00,3.5944E+00)^{T}\) | 1.4973E − 03 | \((-5.0676E-01,2.1352E-01)^{T}\) | \((9.8677E-01,9.7483E-01)^{T}\) | 2.9988E − 04 | 32 |
19 | \((-1.3256E+00,3.0549E+00)^{T}\) | 4.9450E − 04 | \((-3.8494E-02,-1.5711E-02)^{T}\) | \((9.9534E-01,9.9068E-01)^{T}\) | 2.1754E − 05 | 26 |
20 | \((4.8798E+00,7.6720E-01)^{T}\) | 2.7269E − 02 | \((1.7832E+00,-8.3048E-01)^{T}\) | \((1.0529E+00,1.1046E+00)^{T}\) | 4.4787E − 03 | 25 |
21 | \((-4.6226E+00,-3.1708E+00)^{T}\) | 1.0522E − 43 | \((-6.8375E-03,-2.4455E-03)^{T}\) | \((1.0273E+00,1.0554E+00)^{T}\) | 7.4551E − 04 | 17 |
22 | \((3.8517E+00,-2.6007E+00)^{T}\) | 5.8588E − 04 | \((-2.8237E-02,-2.4777E-02)^{T}\) | \((9.9117E-01,9.8235E-01)^{T}\) | 7.8430E − 05 | 24 |
23 | \((4.1329E+00,3.8651E+00)^{T}\) | 7.9595E − 04 | \((-3.1541E-02,-2.1954E-02)^{T}\) | \((9.9240E-01,9.8481E-01)^{T}\) | 5.8049E − 05 | 42 |
24 | \((-6.4660E-01,-9.5770E-01)^{T}\) | 1.4184E − 37 | \((-2.6830E-02,-2.2030E-02)^{T}\) | \((9.9485E-01,9.8967E-01)^{T}\) | 2.6847E − 05 | 20 |
25 | \((-4.0129E+00,-1.0100E-01)^{T}\) | 2.2635E − 43 | \((-4.4286E-03,-4.6080E-04)^{T}\) | \((1.0309E+00,1.0628E+00)^{T}\) | 9.5458E − 04 | 30 |
26 | \((-2.3813E+00,-3.3207E+00)^{T}\) | 5.2263E − 40 | \((-1.9932E-02,-1.0626E-02)^{T}\) | \((1.0110E+00,1.0220E+00)^{T}\) | 1.2022E − 04 | 19 |
27 | \((-1.6464E+00,4.7868E+00)^{T}\) | 1.4188E − 03 | \((-3.0516E-02,-1.4897E-02)^{T}\) | \((1.0005E+00,1.0011E+00)^{T}\) | 3.4798E − 07 | 24 |
28 | \((1.7973E+00,2.1269E+00)^{T}\) | 5.9605E − 03 | \((1.1950E+00,-5.6006E-01)^{T}\) | \((1.0465E+00,1.0925E+00)^{T}\) | 2.9181E − 03 | 12 |
29 | \((-3.6345E+00,4.7000E-03)^{T}\) | 2.1807E − 03 | \((-4.5867E-01,2.2021E-01)^{T}\) | \((1.0314E+00,1.0650E+00)^{T}\) | 1.1214E − 03 | 23 |
30 | \((2.2123E+00,-2.8910E-01)^{T}\) | 8.0544E − 41 | \((-2.0036E-02,-4.1951E-03)^{T}\) | \((1.0181E+00,1.0365E+00)^{T}\) | 3.2608E − 04 | 22 |
31 | \((-8.9670E-01,2.5902E+00)^{T}\) | 6.0000E − 04 | \((2.4092E-01,2.4092E-01)^{T}\) | \((1.0351E+00,1.0727E+00)^{T}\) | 1.3913E − 03 | 11 |
32 | \((4.7941E+00,-1.7500E+00)^{T}\) | 2.3004E − 39 | \((-2.2169E-02,-1.1757E-02)^{T}\) | \((1.0085E+00,1.0171E+00)^{T}\) | 7.2274E − 05 | 21 |
33 | \((1.3976E+00,4.5380E+00)^{T}\) | 3.1194E − 01 | \((1.1220E+00,-5.4273E-01)^{T}\) | \((1.0338E+00,1.0661E+00)^{T}\) | 1.8503E − 03 | 19 |
34 | \((3.6020E+00,2.7511E+00)^{T}\) | 8.8939E − 03 | \((1.1476E-01,-1.0254E-01)^{T}\) | \((9.8567E-01,9.7108E-01)^{T}\) | 2.2681E − 04 | 24 |
35 | \((-1.0068E+00,3.3042E+00)^{T}\) | 2.7821E − 03 | \((6.8507E-01,-3.1611E-01)^{T}\) | \((1.0468E+00,1.0943E+00)^{T}\) | 2.4221E − 03 | 19 |
36 | \((4.4101E+00,7.4560E-01)^{T}\) | 6.3994E − 04 | \((-4.2013E-02,-7.5740E-03)^{T}\) | \((1.0023E+00,1.0046E+00)^{T}\) | 5.1517E − 06 | 25 |
37 | \((4.7164E+00,-8.0170E-01)^{T}\) | 1.4569E − 36 | \((-3.8348E-02,-9.5965E-03)^{T}\) | \((1.0021E+00,1.0041E+00)^{T}\) | 4.2179E − 06 | 9 |