From: A nonmonotone hybrid conjugate gradient method for unconstrained optimization
No. | Dim | LY | NMLY2 | NMLY1 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
it | nf | ng | t | it | nf | ng | t | it | nf | ng | t | ||
1 | 3 | 36 | 69 | 48 | 0.0156 | 59 | 137 | 92 | 0.0156 | 40 | 84 | 60 | 0.0156 |
2 | 6 | 147 | 243 | 200 | 0.0468 | 413 | 853 | 697 | 0.1404 | 146 | 270 | 213 | 0.0468 |
3 | 3 | 2 | 5 | 4 | 0 | 4 | 10 | 8 | 0 | 3 | 9 | 8 | 0 |
4 | 2 | 9 | 26 | 13 | 0 | 11 | 48 | 28 | 0 | 13 | 38 | 17 | 0.0312 |
5 | 3 | 15 | 28 | 19 | 0 | 29 | 75 | 68 | 0.0312 | 14 | 35 | 28 | 0 |
6 | 2 | 37 | 61 | 46 | 0.0156 | 28 | 64 | 45 | 0 | 20 | 60 | 30 | 0.0156 |
7 | 4 | 74 | 130 | 100 | 0.0156 | 313 | 623 | 458 | 0.0936 | 62 | 119 | 90 | 0.0156 |
8 | 2 | 44 | 82 | 61 | 0.0156 | 37 | 98 | 70 | 0 | 5 | 25 | 9 | 0.0156 |
9 | 5 | 128 | 233 | 184 | 0.0936 | 181 | 383 | 278 | 0.1404 | 104 | 199 | 153 | 0.078 |
10 | 11 | 3 | 42 | 3 | 0.0156 | 4 | 29 | 4 | 0 | 3 | 13 | 3 | 0.0312 |
11 | 4 | 6 | 49 | 7 | 0 | 169 | 348 | 254 | 0.0468 | 59 | 121 | 77 | 0.0312 |
12 | 3 | 9 | 45 | 14 | 0 | 170 | 456 | 328 | 0.1248 | 13 | 80 | 34 | 0.0156 |
13 | 3 | 25 | 49 | 33 | 0.0156 | 64 | 135 | 101 | 0.0468 | 39 | 75 | 52 | 0.0312 |
14 | 500 | 14 | 70 | 28 | 0.0156 | 10 | 82 | 40 | 0.0156 | 3 | 46 | 10 | 0.0156 |
15 | 500 | 13 | 68 | 14 | 0 | 13 | 118 | 48 | 0.0312 | 17 | 187 | 122 | 0.0156 |
1,000 | 16 | 70 | 16 | 0 | 13 | 87 | 35 | 0.0156 | 19 | 301 | 211 | 0.0312 | |
2,000 | 14 | 58 | 14 | 0.0156 | 15 | 116 | 50 | 0.0156 | 26 | 362 | 237 | 0.0624 | |
16 | 500 | 11 | 35 | 22 | 0.0156 | 40 | 147 | 101 | 0.0156 | 34 | 103 | 87 | 0.0156 |
1,000 | 16 | 40 | 23 | 0 | 49 | 141 | 99 | 0.0312 | 21 | 82 | 62 | 0.0156 | |
2,000 | 20 | 51 | 28 | 0.0312 | 34 | 122 | 73 | 0.0312 | 57 | 156 | 108 | 0.0624 | |
1,000 | 22 | 75 | 30 | 0.078 | 28 | 96 | 67 | 0.1248 | 31 | 134 | 70 | 0.156 | |
17 | 500 | 42 | 87 | 58 | 0.0156 | 133 | 294 | 213 | 0.078 | 3 | 18 | 3 | 0 |
1,000 | 64 | 120 | 87 | 0.0312 | 187 | 406 | 299 | 0.0936 | 3 | 19 | 3 | 0 | |
2,000 | 53 | 105 | 72 | 0.0312 | 134 | 304 | 221 | 0.0936 | 3 | 19 | 3 | 0.0156 | |
1,000 | 56 | 113 | 79 | 0.2028 | 184 | 393 | 292 | 0.624 | 3 | 19 | 3 | 0.0312 | |
18 | 500 | 220 | 364 | 295 | 0.1092 | 184 | 353 | 253 | 0.1092 | 110 | 197 | 160 | 0.0624 |
1,000 | 180 | 288 | 238 | 0.1404 | 163 | 322 | 235 | 0.1404 | 104 | 191 | 150 | 0.078 | |
2,000 | 181 | 308 | 248 | 0.2184 | 181 | 361 | 262 | 0.2496 | 112 | 205 | 164 | 0.156 | |
1,000 | 217 | 361 | 293 | 1.2792 | 320 | 625 | 458 | 2.1372 | 133 | 244 | 197 | 0.8892 | |
19 | 500 | 68 | 105 | 86 | 5.694 | 103 | 210 | 146 | 10.9201 | 70 | 112 | 95 | 6.1308 |
1,000 | 99 | 143 | 125 | 32.7602 | 88 | 185 | 133 | 38.891 | 113 | 201 | 144 | 40.0923 | |
2,000 | 72 | 110 | 95 | 90.5742 | 190 | 387 | 287 | 306.2456 | 78 | 141 | 104 | 110.3239 | |
1,000 | 121 | 197 | 142 | 983.8203 | 35 | 156 | 80 | 708.6189 | 24 | 67 | 45 | 322.8129 | |
20 | 500 | 51 | 74 | 60 | 0.0468 | 55 | 114 | 73 | 0.0156 | 53 | 83 | 68 | 0.0312 |
1,000 | 54 | 78 | 62 | 0.0312 | 55 | 117 | 73 | 0.0312 | 93 | 143 | 115 | 0.0468 | |
2,000 | 44 | 74 | 58 | 0.0312 | 58 | 130 | 87 | 0.0624 | 33 | 61 | 39 | 0.0156 | |
1,000 | 43 | 69 | 57 | 0.1872 | 52 | 115 | 71 | 0.1872 | 42 | 75 | 59 | 0.1248 | |
21 | 500 | 4 | 9 | 8 | 0.0468 | 10 | 20 | 19 | 0.1092 | 8 | 18 | 17 | 0.1092 |
1,000 | 5 | 11 | 10 | 0.234 | 10 | 20 | 19 | 0.468 | 9 | 20 | 19 | 0.468 | |
2,000 | 5 | 11 | 10 | 0.9204 | 10 | 20 | 19 | 1.8408 | 9 | 20 | 19 | 1.8252 | |
1,000 | 5 | 11 | 10 | 6.63 | 11 | 23 | 22 | 15.3973 | 10 | 21 | 20 | 13.8997 | |
22 | 500 | 50 | 91 | 68 | 1.1076 | 86 | 207 | 133 | 2.2308 | 36 | 92 | 65 | 1.0764 |
1,000 | 33 | 96 | 52 | 3.3852 | 52 | 146 | 100 | 6.552 | 43 | 104 | 71 | 4.602 | |
2,000 | 27 | 113 | 48 | 12.1681 | 43 | 147 | 91 | 23.6186 | 52 | 167 | 83 | 22.9477 | |
1,000 | 102 | 222 | 142 | 246.5128 | 76 | 196 | 140 | 244.2664 | 42 | 123 | 71 | 124.442 | |
23 | 500 | 4 | 32 | 8 | 0.1092 | 13 | 69 | 30 | 0.4368 | 3 | 36 | 6 | 0.078 |
1,000 | 6 | 69 | 9 | 0.4836 | 17 | 230 | 61 | 3.4944 | 3 | 57 | 5 | 0.234 | |
2,000 | 5 | 61 | 8 | 1.794 | 16 | 165 | 41 | 10.3585 | 3 | 37 | 3 | 0.5304 | |
1,000 | 5 | 62 | 11 | 16.1617 | 12 | 125 | 20 | 30.6074 | 3 | 56 | 5 | 6.1932 | |
24 | 500 | 59 | 137 | 88 | 0.0156 | 62 | 232 | 133 | 0.0312 | 34 | 192 | 121 | 0.0156 |
1,000 | 26 | 91 | 34 | 0.0156 | 34 | 174 | 98 | 0.0312 | 56 | 292 | 204 | 0.0624 | |
2,000 | 17 | 68 | 26 | 0.0156 | 16 | 112 | 35 | 0.0312 | 22 | 272 | 172 | 0.0624 | |
1,000 | 37 | 89 | 42 | 0.1092 | 34 | 164 | 59 | 0.156 | 25 | 266 | 146 | 0.2496 | |
25 | 500 | 7 | 67 | 43 | 12.8545 | 13 | 85 | 53 | 15.9589 | 13 | 80 | 26 | 10.4521 |
1,000 | 7 | 59 | 28 | 26.7698 | 8 | 78 | 51 | 41.9019 | 47 | 229 | 130 | 115.8931 | |
2,000 | 22 | 141 | 90 | 275.5914 | 7 | 55 | 28 | 96.081 | 7 | 68 | 28 | 107.2507 | |
1,000 | 7 | 63 | 36 | 716.4346 | 16 | 175 | 117 | 2148.9606 | 11 | 115 | 63 | 1265.6829 | |
26 | 500 | 54 | 105 | 77 | 1.6224 | 55 | 127 | 88 | 1.7628 | 46 | 97 | 68 | 1.3728 |
1,000 | 53 | 101 | 75 | 5.4132 | 92 | 195 | 140 | 10.4053 | 46 | 94 | 69 | 5.0856 | |
2,000 | 42 | 89 | 62 | 15.1945 | 71 | 162 | 113 | 27.5654 | 40 | 92 | 65 | 16.0213 | |
1,000 | 29 | 68 | 43 | 44.4603 | 58 | 150 | 105 | 110.0275 | 44 | 97 | 68 | 69.7168 | |
27 | 500 | 3 | 52 | 4 | 0.2184 | 11 | 178 | 91 | 1.9968 | 9 | 152 | 12 | 0.6708 |
1,000 | 13 | 193 | 99 | 8.7049 | 5 | 68 | 13 | 1.5756 | 7 | 106 | 27 | 2.9484 | |
2,000 | 5 | 101 | 46 | 16.3645 | 7 | 141 | 40 | 16.5205 | 7 | 141 | 48 | 18.7045 | |
1,000 | 9 | 112 | 32 | 99.279 | 8 | 140 | 33 | 112.5859 | 13 | 224 | 48 | 172.6151 | |
28 | 500 | 8 | 23 | 10 | 0 | 22 | 60 | 38 | 0.0468 | 19 | 45 | 27 | 0.0156 |
1,000 | 9 | 25 | 13 | 0.0156 | 7 | 45 | 31 | 0.0156 | 11 | 59 | 43 | 0.0312 | |
2,000 | 16 | 60 | 26 | 0.0312 | 13 | 78 | 42 | 0.0624 | 16 | 72 | 36 | 0.0468 | |
1,000 | 5 | 22 | 7 | 0.0312 | 10 | 53 | 30 | 0.2496 | 11 | 60 | 40 | 0.2808 | |
29 | 500 | 28 | 65 | 41 | 0.0468 | 13 | 69 | 52 | 0.0312 | 13 | 50 | 27 | 0.0312 |
1,000 | 4 | 17 | 5 | 0 | 22 | 86 | 53 | 0.0468 | 11 | 56 | 34 | 0.0156 | |
2,000 | 7 | 23 | 8 | 0 | 10 | 49 | 26 | 0.0468 | 13 | 66 | 35 | 0.0468 | |
1,000 | 7 | 26 | 9 | 0.0624 | 4 | 40 | 28 | 0.156 | 12 | 124 | 101 | 0.7332 | |
30 | 500 | 287 | 452 | 387 | 14.6017 | 365 | 691 | 649 | 21.0913 | 249 | 380 | 334 | 10.1089 |
1,000 | 292 | 456 | 407 | 44.5071 | 343 | 646 | 593 | 69.3736 | 257 | 404 | 359 | 40.8411 | |
2,000 | 343 | 524 | 477 | 154.3786 | 376 | 721 | 655 | 213.9242 | 271 | 457 | 376 | 122.1176 | |
1,000 | 310 | 474 | 424 | 640.2749 | 376 | 729 | 663 | 1006.2533 | 236 | 412 | 337 | 512.9157 | |
31 | 500 | 70 | 110 | 87 | 0.3276 | 73 | 158 | 113 | 0.39 | 58 | 115 | 90 | 0.2964 |
1,000 | 49 | 88 | 66 | 0.468 | 50 | 131 | 93 | 0.624 | 30 | 68 | 45 | 0.312 | |
2,000 | 38 | 69 | 49 | 0.7644 | 64 | 142 | 103 | 1.3416 | 34 | 75 | 49 | 0.6396 | |
1,000 | 27 | 52 | 32 | 2.0904 | 53 | 128 | 90 | 6.1152 | 34 | 85 | 60 | 4.0248 | |
32 | 500 | 6 | 50 | 9 | 0.0156 | 53 | 144 | 89 | 0.0624 | 4 | 60 | 6 | 0 |
1,000 | 30 | 88 | 44 | 0.0468 | 18 | 211 | 35 | 0.0468 | 6 | 93 | 7 | 0.0156 | |
2,000 | 3 | 23 | 6 | 0.0156 | 10 | 107 | 16 | 0.0468 | 4 | 45 | 5 | 0.0156 | |
1,000 | 5 | 39 | 10 | 0.0936 | 8 | 80 | 17 | 0.1872 | 4 | 55 | 8 | 0.0936 | |
33 | 500 | 320 | 442 | 406 | 7.6596 | 427 | 822 | 614 | 11.8405 | 4 | 24 | 7 | 0.1248 |
1,000 | 268 | 381 | 342 | 20.6233 | 338 | 652 | 483 | 29.1566 | 4 | 25 | 7 | 0.39 | |
2,000 | 195 | 269 | 248 | 47.1435 | 235 | 461 | 342 | 66.7996 | 4 | 25 | 7 | 1.2792 | |
1,000 | 145 | 198 | 182 | 137.4681 | 223 | 434 | 326 | 247.1524 | 4 | 25 | 7 | 4.5396 | |
34 | 500 | 105 | 187 | 146 | 0.1404 | 101 | 234 | 162 | 0.156 | 98 | 191 | 143 | 0.1404 |
1,000 | 33 | 76 | 49 | 0.1248 | 73 | 197 | 136 | 0.2496 | 97 | 203 | 156 | 0.2028 | |
2,000 | 123 | 226 | 172 | 0.39 | 173 | 416 | 306 | 0.6708 | 89 | 196 | 141 | 0.312 | |
1,000 | 175 | 311 | 243 | 2.6676 | 236 | 537 | 395 | 4.6176 | 151 | 319 | 239 | 2.6676 | |
35 | 500 | 12 | 25 | 14 | 0.0468 | 13 | 35 | 23 | 0.078 | 5 | 18 | 5 | 0.0156 |
1,000 | 12 | 25 | 14 | 0.078 | 11 | 30 | 19 | 0.1248 | 5 | 18 | 5 | 0.0312 | |
2,000 | 11 | 23 | 13 | 0.1716 | 11 | 34 | 23 | 0.2808 | 5 | 18 | 5 | 0.0624 | |
1,000 | 10 | 23 | 14 | 0.9984 | 10 | 31 | 22 | 1.56 | 5 | 18 | 5 | 0.2808 | |
36 | 500 | 37 | 228 | 122 | 0.6864 | 10 | 78 | 17 | 0.1404 | 9 | 34 | 16 | 0.078 |
1,000 | 17 | 75 | 25 | 0.2652 | 11 | 78 | 20 | 0.234 | 9 | 51 | 13 | 0.156 | |
2,000 | 37 | 137 | 57 | 1.1076 | 11 | 101 | 21 | 0.5148 | 15 | 90 | 34 | 0.6864 | |
1,000 | 16 | 82 | 23 | 2.496 | 10 | 82 | 18 | 2.1684 | 15 | 76 | 21 | 2.106 | |
37 | 500 | 11 | 25 | 16 | 0.0156 | 10 | 33 | 19 | 0 | 3 | 17 | 6 | 0 |
1,000 | 12 | 26 | 15 | 0.0156 | 11 | 29 | 19 | 0.0156 | 3 | 17 | 6 | 0 | |
2,000 | 10 | 22 | 12 | 0.0312 | 10 | 27 | 18 | 0.0312 | 3 | 18 | 6 | 0.0156 | |
5,000 | 8 | 18 | 10 | 0.0936 | 10 | 27 | 18 | 0.156 | 3 | 18 | 6 | 0.0624 | |
38 | 500 | 6 | 75 | 50 | 0.0156 | 10 | 123 | 72 | 0.0624 | 8 | 105 | 51 | 0.0312 |
1,000 | 4 | 63 | 22 | 0.0156 | 7 | 107 | 43 | 0.0468 | 4 | 56 | 24 | 0.0156 | |
2,000 | 7 | 121 | 65 | 0.0624 | 13 | 211 | 130 | 0.1248 | 8 | 132 | 68 | 0.078 | |
5,000 | 5 | 95 | 49 | 0.2184 | 5 | 84 | 34 | 0.156 | 6 | 115 | 51 | 0.2496 | |
39 | 500 | 8 | 127 | 51 | 2.7924 | 10 | 168 | 76 | 3.7596 | 9 | 127 | 62 | 3.042 |
1,000 | 7 | 107 | 40 | 8.5021 | 11 | 188 | 85 | 15.7405 | 9 | 144 | 61 | 11.9341 | |
2,000 | 10 | 142 | 67 | 46.7691 | 16 | 248 | 104 | 81.2453 | 113 | 573 | 189 | 182.7708 | |
5,000 | 9 | 165 | 72 | 698.6037 | 12 | 162 | 78 | 675.7495 | 13 | 181 | 83 | 756.8077 | |
40 | 500 | 170 | 257 | 218 | 0.1092 | 305 | 578 | 430 | 0.1716 | 105 | 171 | 140 | 0.1404 |
1,000 | 153 | 231 | 196 | 0.0624 | 265 | 505 | 367 | 0.1404 | 114 | 208 | 155 | 0.0624 | |
2,000 | 147 | 222 | 190 | 0.0936 | 272 | 522 | 390 | 0.1872 | 117 | 188 | 155 | 0.078 | |
5,000 | 144 | 233 | 184 | 0.3588 | 305 | 579 | 425 | 0.8424 | 125 | 205 | 172 | 0.3276 |