Theory and Modern Applications
Table 2 Numerical results of the RMIL, RMIL+, and PRP methods using weak Wolfe line search
Number | RMIL | RMIL+ | PRP | ||||||
|---|---|---|---|---|---|---|---|---|---|
NOI | NOF | CPU | NOI | NOF | CPU | NOI | NOF | CPU | |
1 | 25 | 160 | 0.075 | 16 | 102 | 0.0588 | 15 | 104 | 0.0525 |
2 | F | F | F | F | F | F | 21 | 181 | 0.0898 |
3 | 25 | 160 | 0.578 | 16 | 102 | 0.3907 | 15 | 104 | 0.3841 |
4 | F | F | F | 38 | 260 | 0.9512 | 22 | 203 | 0.7392 |
5 | F | F | F | 27 | 176 | 0.0488 | 19 | 123 | 0.0377 |
6 | 44 | 227 | 0.0618 | 40 | 243 | 0.0667 | F | F | F |
7 | F | F | F | 32 | 192 | 0.3874 | 19 | 123 | 0.231 |
8 | 24 | 126 | 0.2573 | 40 | 195 | 0.3768 | 20 | 136 | 0.4796 |
9 | F | F | F | 11 | 63 | 0.1356 | 8 | 54 | 0.1141 |
10 | F | F | F | 11 | 63 | 0.4922 | 8 | 54 | 0.3937 |
11 | 41 | 137 | 0.5728 | 52 | 191 | 0.0992 | 15 | 69 | 0.0479 |
12 | 56 | 175 | 0.0987 | F | F | F | 9 | 44 | 0.0367 |
13 | 22 | 83 | 0.3537 | 11 | 48 | 0.2153 | F | F | F |
14 | 58 | 182 | 0.7956 | F | F | F | 10 | 47 | 0.222 |
15 | 24 | 83 | 0.0015 | 27 | 105 | 0.0026 | 22 | 87 | 0.0021 |
16 | 36 | 143 | 0.0022 | 37 | 170 | 0.0062 | 37 | 157 | 0.0036 |
17 | 110 | 333 | 0.0379 | 109 | 505 | 0.0394 | 74 | 409 | 0.032 |
18 | 140 | 435 | 0.0439 | 180 | 841 | 0.0609 | F | F | F |
19 | 12 | 56 | 0.0203 | 6 | 37 | 0.0144 | F | F | F |
20 | F | F | F | 5 | 26 | 0.0145 | 5 | 26 | 0.0139 |
21 | 12 | 56 | 0.0412 | 7 | 40 | 0.0276 | F | F | F |
22 | 8 | 41 | 0.0379 | 9 | 55 | 0.0425 | 13 | 68 | 0.0458 |
23 | F | F | F | F | F | F | F | F | F |
24 | F | F | F | F | F | F | F | F | F |
25 | F | F | F | F | F | F | F | F | F |
26 | F | F | F | F | F | F | F | F | F |
27 | 12 | 43 | 0.0205 | 11 | 44 | 0.0215 | 8 | 34 | 0.0327 |
28 | 10 | 48 | 0.0196 | 7 | 34 | 0.0165 | 6 | 31 | 0.0127 |
29 | 9 | 39 | 0.0942 | 9 | 42 | 0.0952 | 8 | 45 | 0.1075 |
30 | F | F | F | 11 | 50 | 0.137 | 8 | 44 | 0.1027 |
31 | 72 | 289 | 0.0036 | 72 | 311 | 0.0084 | 56 | 263 | 0.0055 |
32 | 138 | 712 | 0.0198 | 111 | 548 | 0.0183 | 71 | 376 | 0.0078 |
33 | F | F | F | 70 | 863 | 0.0716 | 3337 | 10,084 | 0.7111 |
34 | F | F | F | 39 | 225 | 0.0443 | 2312 | 7053 | 0.4623 |
35 | 8 | 34 | 4.81E − 04 | 54 | 193 | 0.0183 | 15 | 76 | 0.0048 |
36 | F | F | F | 17 | 94 | 0.2085 | F | F | F |
37 | 7 | 22 | 4.32E − 04 | 6 | 22 | 0.000845 | 5 | 19 | 0.0042 |
38 | 8 | 33 | 5.90E − 04 | 8 | 37 | 0.0022 | 8 | 37 | 0.0023 |
39 | 8 | 33 | 0.0038 | 8 | 37 | 0.0093 | 8 | 37 | 0.0044 |
40 | 11 | 52 | 0.0172 | 9 | 43 | 0.0181 | 7 | 37 | 0.0032 |
41 | F | F | F | 27 | 112 | 0.0038 | 31 | 117 | 0.0017 |
42 | F | F | F | 26 | 103 | 0.0021 | 9 | 46 | 6.12E−04 |
43 | 26 | 123 | 0.0081 | 19 | 87 | 0.0056 | 12 | 82 | 0.006 |
44 | F | F | F | 19 | 89 | 0.0124 | 13 | 87 | 0.0077 |
45 | F | F | F | F | F | F | F | F | F |
46 | F | F | F | F | F | F | F | F | F |
47 | F | F | F | 207 | 923 | 0.0331 | F | F | F |
48 | 40 | 191 | 0.0126 | 31 | 195 | 0.0134 | 25 | 188 | 0.004 |
49 | 9 | 39 | 0.0005699 | 8 | 36 | 0.0053 | 6 | 30 | 0.007 |
50 | 10 | 59 | 0.0081 | 11 | 66 | 0.0026 | F | F | F |
51 | 15 | 363 | 0.0034 | F | F | F | F | F | F |
52 | 11 | 226 | 0.0075 | 15 | 400 | 0.0108 | F | F | F |
53 | 2 | 6 | 0.0001505 | 2 | 6 | 2.58E − 04 | 2 | 6 | 2.34E−04 |
54 | 2 | 6 | 0.0105 | 2 | 6 | 2.84E − 04 | 2 | 6 | 4.06E−04 |
55 | 1 | 3 | 0.0002193 | 1 | 3 | 0.0013 | 1 | 3 | 1.95E−04 |
56 | F | F | F | 5 | 23 | 0.007 | 5 | 23 | 6.89E−04 |
57 | 18 | 66 | 0.0024 | 16 | 69 | 0.0028 | 10 | 45 | 0.0011 |
58 | 12 | 46 | 0.0075 | F | F | F | 12 | 59 | 0.0012 |
59 | 14 | 46 | 0.0209 | 11 | 39 | 0.0154 | F | F | F |
60 | 16 | 58 | 0.035 | 14 | 59 | 0.0303 | 13 | 51 | 0.018 |
61 | 51 | 155 | 0.3235 | F | F | F | F | F | F |
62 | F | F | F | F | F | F | F | F | F |
63 | 24 | 301 | 0.0146 | F | F | F | F | F | F |
64 | F | F | F | F | F | F | F | F | F |
65 | 78 | 265 | 0.0146 | 78 | 280 | 0.0225 | 70 | 250 | 0.0241 |
66 | 78 | 299 | 0.0226 | 77 | 334 | 0.0327 | 58 | 275 | 0.0322 |
67 | 35 | 170 | 0.0046 | 31 | 179 | 0.0023 | 17 | 136 | 0.0012 |
68 | F | F | F | 35 | 265 | 0.0033 | 28 | 243 | 0.0032 |
69 | 21 | 66 | 0.0019 | 22 | 74 | 0.0058 | 23 | 77 | 0.0057 |
70 | 27 | 104 | 0.0155 | 28 | 120 | 0.003 | 27 | 117 | 0.0037 |
71 | F | F | F | 7 | 21 | 0.0027 | F | F | F |
72 | F | F | F | F | F | F | 11 | 59 | 0.0019 |
73 | 123 | 369 | 0.0074 | 123 | 369 | 0.0102 | 10 | 30 | 7.66E−04 |
74 | 139 | 417 | 0.0139 | 139 | 417 | 0.0123 | 10 | 30 | 8.78E−04 |
75 | 69 | 207 | 0.0108 | 69 | 207 | 0.0115 | 38 | 114 | 0.0049 |
76 | 78 | 234 | 0.0093 | 78 | 234 | 0.0104 | 40 | 120 | 0.0073 |
77 | 447 | 1341 | 0.1754 | 447 | 1341 | 0.1716 | 131 | 393 | 0.0719 |
78 | 500 | 1500 | 0.2143 | 500 | 1500 | 0.2046 | 137 | 411 | 0.072 |
79 | 37 | 314 | 0.0274 | 34 | 313 | 0.0254 | 22 | 235 | 0.0161 |
80 | F | F | F | 30 | 296 | 0.0252 | 27 | 296 | 0.0233 |
81 | 60 | 591 | 0.099 | 57 | 620 | 0.1127 | 39 | 493 | 0.087 |
82 | 3899 | 12030 | 1.6296 | 69 | 743 | 0.1158 | 43 | 528 | 0.082 |
83 | 14 | 48 | 0.0009078 | 14 | 53 | 0.0012 | 6 | 28 | 6.26E−04 |
84 | 20 | 81 | 0.0144 | 15 | 68 | 0.0013 | 9 | 49 | 9.52E−04 |
85 | 773 | 2468 | 0.0345 | 802 | 2788 | 0.0517 | 163 | 696 | 0.0138 |
86 | 781 | 2558 | 0.0395 | 806 | 2811 | 0.0454 | 113 | 495 | 0.0133 |
87 | F | F | F | F | F | F | F | F | F |
88 | F | F | F | F | F | F | F | F | F |
89 | 773 | 3091 | 0.0378 | 1032 | 4339 | 0.0726 | 148 | 818 | 0.2155 |
90 | 897 | 3418 | 0.0425 | 669 | 2819 | 0.0324 | 86 | 372 | 0.0167 |
91 | 42 | 149 | 0.0077 | F | F | F | F | F | F |
92 | 35 | 141 | 0.0196 | 46 | 194 | 0.0083 | 56 | 266 | 0.0063 |
93 | 1 | 3 | 0.0057 | 1 | 3 | 0.0083 | 1 | 3 | 0.0167 |
94 | 1 | 3 | 0.0179 | 1 | 3 | 0.0056 | 1 | 3 | 0.0071 |
95 | 46 | 138 | 0.0123 | 46 | 138 | 0.0152 | 25 | 75 | 0.0057 |
96 | 81 | 243 | 0.5261 | 81 | 243 | 0.2223 | 41 | 123 | 0.0097 |
97 | 23 | 112 | 0.0162 | 47 | 817 | 0.0301 | 22 | 409 | 0.0147 |
98 | F | F | F | F | F | F | 22 | 416 | 0.0251 |
99 | 14 | 46 | 0.0112 | 14 | 63 | 0.2976 | 14 | 78 | 0.2305 |
100 | 14 | 60 | 0.0089 | F | F | F | F | F | F |
101 | F | F | F | F | F | F | F | F | F |
102 | F | F | F | F | F | F | F | F | F |
103 | F | F | F | F | F | F | F | F | F |
104 | F | F | F | F | F | F | F | F | F |