Table 3 Numerical results of Example 5.2 using classical PRP Algorithm
From: A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems
Sl. no. | Starting point | PRP algorithm | ||||
|---|---|---|---|---|---|---|
Step-length | Gradient | \(x^{*}\) | \(f(x^{*})\) | NI | ||
1 | \((-4.1448E+00,-2.9324E+00)^{T}\) | 1.0472E − 03 | \((1.0287E-07,-8.3547E-09)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 5.3298E − 16 | 41 |
2 | \((-4.2752E+00,-2.8376E+00)^{T}\) | 1.9542E − 03 | \((3.1505E-07,-9.3225E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 6.3375E − 13 | 51 |
3 | \((3.0101E+00,-5.8300E-02)^{T}\) | 1.0721E − 03 | \((-2.7082E-07,-1.2131E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 7.6609E − 14 | 39 |
4 | \((2.4348E+00,-2.8090E+00)^{T}\) | 1.1164E − 03 | \((9.4822E-08,2.0076E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 2.2560E − 15 | 27 |
5 | \((2.4944E+00,8.7790E-01)^{T}\) | 1.4495E − 03 | \((-3.8184E-07,-8.9269E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 9.0135E − 14 | 57 |
6 | \((2.3033E+00,4.0372E+00)^{T}\) | 1.2433E − 03 | \((-1.5568E-09,-5.8448E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 3.6719E − 13 | 30 |
7 | \((-1.1390E-01,3.9092E+00)^{T}\) | 1.5078E − 03 | \((-2.0814E-07,7.1389E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 3.4916E − 13 | 65 |
8 | \((-2.7857E+00,1.0782E+00)^{T}\) | 1.2141E − 03 | \((-4.8623E-07,3.7559E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 1.3003E − 14 | 45 |
9 | \((-2.6272E+00,1.9875E+00)^{T}\) | 1.2900E − 03 | \((-8.2621E-07,5.7665E-09)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 1.8262E − 13 | 54 |
10 | \((-4.1150E-01,-3.0219E+00)^{T}\) | 1.0185E − 03 | \((1.7739E-09,-2.8126E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 2.2335E − 15 | 31 |
11 | \((4.6309E+00,-4.6946E+00)^{T}\) | 1.6958E − 03 | \((1.0000E+00,1.0000E+00)^{T}\) | \((7.0029E-07,1.8475E-07)^{T}\) | 2.6520E − 13 | 51 |
12 | \((4.6810E-01,2.4407E+00)^{T}\) | 1.5815E − 03 | \((-5.8657E-07,5.9774E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 8.1809E − 14 | 60 |
13 | \((2.1140E-01,2.0000E-04)^{T}\) | 1.1507E − 03 | \((-8.3793E-07,7.7501E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 1.3067E − 13 | 27 |
14 | \((-2.6841E+00,-2.0080E-01)^{T}\) | 1.1155E − 03 | \((3.5193E-07,1.1527E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 7.3605E − 14 | 32 |
15 | \((-1.1100E-01,4.0472E+00)^{T}\) | 1.2035E − 03 | \((5.3046E-09,-3.8049E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 1.5864E − 13 | 49 |
16 | \((1.2406E+00,1.0987E+00)^{T}\) | 1.0736E − 03 | \((-1.5669E-07,3.9305E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 3.4898E − 15 | 35 |
17 | \((1.7914E+00,1.1767E+00)^{T}\) | 1.1084E − 03 | \((-4.2829E-07,-3.1031E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 7.0320E − 14 | 54 |
18 | \((-1.0448E+00,3.5944E+00)^{T}\) | 1.0011E − 03 | \((3.3377E-08,4.1644E-10)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 8.3811E − 18 | 36 |
19 | \((-1.3256E+00,3.0549E+00)^{T}\) | 1.3002E − 03 | \((-3.4159E-07,1.5132E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 3.0857E − 14 | 45 |
20 | \((4.8798E+00,7.6720E-01)^{T}\) | 1.0964E − 03 | \((1.0605E-07,6.6228E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 4.8455E − 13 | 54 |
21 | \((-4.6226E+00,-3.1708E+00)^{T}\) | 1.1278E − 03 | \((-9.7930E-07,-1.3147E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 4.1108E − 13 | 39 |
22 | \((3.8517E+00,-2.6007E+00)^{T}\) | 1.2356E − 03 | \((2.6266E-07,-3.7627E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 7.0545E − 14 | 63 |
23 | \((4.1329E+00,3.8651E+00)^{T}\) | 9.9963E − 04 | \((-1.1176E-07,-2.4588E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 1.0368E − 13 | 36 |
24 | \((-6.4660E-01,-9.5770E-01)^{T}\) | 1.2494E − 03 | \((-2.7319E-07,-1.3338E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 8.4128E − 14 | 60 |
25 | \((-4.0129E+00,-1.0100E-01)^{T}\) | 1.0451E − 03 | \((5.1172E-10,8.1593E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 6.3558E − 13 | 37 |
26 | \((-2.3813E+00,-3.3207E+00)^{T}\) | 1.0864E − 03 | \((1.7723E-07,-3.3755E-09)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 4.2562E − 15 | 31 |
27 | \((-1.6464E+00,4.7868E+00)^{T}\) | 1.4132E − 03 | \((2.7136E-07,-7.2242E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 3.6945E − 13 | 53 |
28 | \((1.7973E+00,2.1269E+00)^{T}\) | 1.0040E − 03 | \((7.7808E-09,-7.7013E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 8.6866E − 15 | 32 |
29 | \((-3.6345E+00,4.7000E-03)^{T}\) | 1.0004E − 03 | \((8.2682E-07,2.2167E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 3.7845E − 13 | 22 |
30 | \((2.2123E+00,-2.8910E-01)^{T}\) | 1.0979E − 03 | \((3.6809E-08,-7.3394E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 5.6368E − 15 | 51 |
31 | \((-8.9670E-01,2.5902E+00)^{T}\) | 1.3091E − 03 | \((-7.9028E-07,6.0042E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 3.5229E − 14 | 50 |
32 | \((4.7941E+00,-1.7500E+00)^{T}\) | 1.0964E − 03 | \((-4.7745E-08,2.1303E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 2.8729E − 14 | 33 |
33 | \((1.3976E+00,4.5380E+00)^{T}\) | 1.1476E − 03 | \((2.2973E-07,1.9974E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 1.3189E − 14 | 38 |
34 | \((3.6020E+00,2.7511E+00)^{T}\) | 1.0413E − 03 | \((4.0635E-07,-7.6268E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 1.1443E − 14 | 37 |
35 | \((-1.0068E+00,3.3042E+00)^{T}\) | 1.2183E − 03 | \((5.3450E-07,1.5490E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 1.6179E − 13 | 37 |
36 | \((4.4101E+00,7.4560E-01)^{T}\) | 1.0686E − 03 | \((-4.8905E-08,2.0217E-07)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 2.4978E − 14 | 35 |
37 | \((4.7164E+00,-8.0170E-01)^{T}\) | 1.2984E − 03 | \((-9.3419E-07,-5.7970E-08)^{T}\) | \((1.0000E+00,1.0000E+00)^{T}\) | 2.9711E − 13 | 37 |