Research Article
Modified Three-Term Liu–Storey Conjugate Gradient Method for Solving Unconstrained Optimization Problems and Image Restoration Problems
Table 2
Test results of the NLS algorithm.
| Nr | Dim | NLS algorithm | NI | NFG | CPU |
| 1 | 3000 | 5 | 26 | 0.125 | 1 | 6000 | 5 | 26 | 0.140625 | 1 | 9000 | 5 | 26 | 0.21875 | 2 | 3000 | 92 | 428 | 4.078125 | 2 | 6000 | 102 | 472 | 7.15625 | 2 | 9000 | 97 | 457 | 7.84375 | 3 | 3000 | 6 | 32 | 0.0625 | 3 | 6000 | 6 | 32 | 0 | 3 | 9000 | 6 | 32 | 0 | 4 | 3000 | 5 | 26 | 0.0625 | 4 | 6000 | 5 | 26 | 0.109375 | 4 | 9000 | 5 | 26 | 0.109375 | 5 | 3000 | 5 | 26 | 0.0625 | 5 | 6000 | 5 | 26 | 0.0625 | 5 | 9000 | 5 | 26 | 0.0625 | 6 | 3000 | 4 | 20 | 0 | 6 | 6000 | 4 | 20 | 0.0625 | 6 | 9000 | 4 | 20 | 0.0625 | 7 | 3000 | 83 | 361 | 0.125 | 7 | 6000 | 85 | 370 | 0.25 | 7 | 9000 | 86 | 377 | 0.34375 | 8 | 3000 | 1000 | 3046 | 2.078125 | 8 | 6000 | 10 | 40 | 0.0625 | 8 | 9000 | 10 | 40 | 0.0625 | 9 | 3000 | 6 | 20 | 0.0625 | 9 | 6000 | 6 | 20 | 0 | 9 | 9000 | 6 | 20 | 0.0625 | 10 | 3000 | 3 | 14 | 0 | 10 | 6000 | 3 | 14 | 0 | 10 | 9000 | 3 | 14 | 0.0625 | 11 | 3000 | 1000 | 2999 | 2.8125 | 11 | 6000 | 1000 | 2999 | 5.296875 | 11 | 9000 | 1000 | 2999 | 7.8125 | 12 | 3000 | 3 | 14 | 0 | 12 | 6000 | 3 | 14 | 0.03125 | 12 | 9000 | 3 | 14 | 0 | 13 | 3000 | 4 | 17 | 0 | 13 | 6000 | 4 | 17 | 0.0625 | 13 | 9000 | 4 | 20 | 0.0625 | 14 | 3000 | 7 | 38 | 0.203125 | 14 | 6000 | 7 | 38 | 0.375 | 14 | 9000 | 7 | 38 | 0.453125 | 15 | 3000 | 7 | 38 | 0.1875 | 15 | 6000 | 7 | 38 | 0.3125 | 15 | 9000 | 7 | 38 | 0.34375 | 16 | 3000 | 4 | 20 | 0 | 16 | 6000 | 4 | 20 | 0 | 16 | 9000 | 4 | 20 | 0.0625 | 17 | 3000 | 5 | 26 | 0.125 | 17 | 6000 | 5 | 26 | 0.140625 | 17 | 9000 | 5 | 26 | 0.234375 | 18 | 3000 | 1000 | 3075 | 0.75 | 18 | 6000 | 1000 | 3075 | 1.234375 | 18 | 9000 | 1000 | 3075 | 2.046875 | 19 | 3000 | 10 | 29 | 0 | 19 | 6000 | 10 | 29 | 0.0625 | 19 | 9000 | 10 | 29 | 0.1875 | 20 | 3000 | 7 | 38 | 0.0625 | 20 | 6000 | 7 | 38 | 0.0625 | 20 | 9000 | 7 | 38 | 0.0625 | 21 | 3000 | 6 | 32 | 0.125 | 21 | 6000 | 6 | 32 | 0.265625 | 21 | 9000 | 6 | 32 | 0.375 | 22 | 3000 | 9 | 50 | 0.1875 | 22 | 6000 | 9 | 50 | 0.25 | 22 | 9000 | 9 | 50 | 0.28125 | 23 | 3000 | 6 | 32 | 0.0625 | 23 | 6000 | 6 | 32 | 0.125 | 23 | 9000 | 6 | 32 | 0.125 | 24 | 3000 | 505 | 1535 | 1.109375 | 24 | 6000 | 529 | 1607 | 2.3125 | 24 | 9000 | 542 | 1646 | 3.515625 | 25 | 3000 | 6 | 32 | 0.0625 | 25 | 6000 | 6 | 32 | 0 | 25 | 9000 | 6 | 32 | 0.046875 | 26 | 3000 | 4 | 14 | 0 | 26 | 6000 | 4 | 14 | 0.0625 | 26 | 9000 | 4 | 14 | 0 | 27 | 3000 | 84 | 365 | 0.125 | 27 | 6000 | 85 | 370 | 0.3125 | 27 | 9000 | 85 | 372 | 0.359375 | 28 | 3000 | 5 | 26 | 0.0625 | 28 | 6000 | 5 | 26 | 0 | 28 | 9000 | 5 | 26 | 0.03125 | 29 | 3000 | 7 | 38 | 0 | 29 | 6000 | 7 | 38 | 0 | 29 | 9000 | 7 | 38 | 0.0625 | 30 | 3000 | 83 | 357 | 0.0625 | 30 | 6000 | 83 | 361 | 0.1875 | 30 | 9000 | 84 | 366 | 0.21875 | 31 | 3000 | 5 | 26 | 0.0625 | 31 | 6000 | 5 | 26 | 0 | 31 | 9000 | 5 | 26 | 0 | 32 | 3000 | 5 | 26 | 0.125 | 32 | 6000 | 5 | 26 | 0.125 | 32 | 9000 | 5 | 26 | 0.125 | 33 | 3000 | 6 | 32 | 0.0625 | 33 | 6000 | 6 | 32 | 0 | 33 | 9000 | 6 | 32 | 0.0625 | 34 | 3000 | 5 | 26 | 0.0625 | 34 | 6000 | 5 | 26 | 0 | 34 | 9000 | 5 | 26 | 0 | 35 | 3000 | 7 | 33 | 0 | 35 | 6000 | 7 | 33 | 0 | 35 | 9000 | 7 | 33 | 0.0625 | 36 | 3000 | 5 | 26 | 0.125 | 36 | 6000 | 5 | 26 | 0.125 | 36 | 9000 | 5 | 26 | 0.1875 | 37 | 3000 | 87 | 384 | 0.125 | 37 | 6000 | 90 | 398 | 0.25 | 37 | 9000 | 89 | 396 | 0.390625 | 38 | 3000 | 5 | 26 | 0.0625 | 38 | 6000 | 5 | 26 | 0 | 38 | 9000 | 5 | 26 | 0.0625 | 39 | 3000 | 5 | 26 | 0.0625 | 39 | 6000 | 5 | 26 | 0 | 39 | 9000 | 5 | 26 | 0.046875 | 40 | 3000 | 5 | 26 | 0.125 | 40 | 6000 | 5 | 26 | 0.140625 | 40 | 9000 | 5 | 26 | 0.25 | 41 | 3000 | 79 | 334 | 0.125 | 41 | 6000 | 79 | 334 | 0.171875 | 41 | 9000 | 79 | 334 | 0.25 | 42 | 3000 | 46 | 235 | 0.25 | 42 | 6000 | 39 | 204 | 0.4375 | 42 | 9000 | 55 | 272 | 0.71875 | 43 | 3000 | 5 | 26 | 0.125 | 43 | 6000 | 5 | 26 | 0.25 | 43 | 9000 | 5 | 26 | 0.3125 | 44 | 3000 | 5 | 26 | 0.125 | 44 | 6000 | 5 | 26 | 0.15625 | 44 | 9000 | 5 | 26 | 0.28125 | 45 | 3000 | 5 | 26 | 0.109375 | 45 | 6000 | 5 | 26 | 0.203125 | 45 | 9000 | 5 | 26 | 0.3125 | 46 | 3000 | 5 | 26 | 0.078125 | 46 | 6000 | 5 | 26 | 0.21875 | 46 | 9000 | 5 | 26 | 0.375 | 47 | 3000 | 88 | 390 | 6.078125 | 47 | 6000 | 91 | 406 | 19.84375 | 47 | 9000 | 92 | 415 | 41.73438 | 48 | 3000 | 6 | 32 | 0.125 | 48 | 6000 | 6 | 32 | 0.1875 | 48 | 9000 | 6 | 32 | 0.234375 | 49 | 3000 | 83 | 361 | 0.125 | 49 | 6000 | 85 | 370 | 0.171875 | 49 | 9000 | 86 | 377 | 0.1875 | 50 | 3000 | 83 | 361 | 1.125 | 50 | 6000 | 85 | 370 | 2.0625 | 50 | 9000 | 86 | 377 | 2.453125 | 51 | 3000 | 7 | 38 | 0.1875 | 51 | 6000 | 7 | 38 | 0.25 | 51 | 9000 | 7 | 38 | 0.296875 | 52 | 3000 | 4 | 20 | 0.0625 | 52 | 6000 | 4 | 20 | 0.0625 | 52 | 9000 | 4 | 20 | 0.015625 | 53 | 3000 | 1000 | 3015 | 1.03125 | 53 | 6000 | 1000 | 3016 | 1.8125 | 53 | 9000 | 1000 | 3016 | 2.859375 | 54 | 3000 | 5 | 26 | 0 | 54 | 6000 | 5 | 26 | 0.0625 | 54 | 9000 | 5 | 26 | 0 | 55 | 3000 | 24 | 74 | 0.1875 | 55 | 6000 | 26 | 80 | 0.421875 | 55 | 9000 | 26 | 80 | 0.515625 | 56 | 3000 | 788 | 2374 | 0.875 | 56 | 6000 | 788 | 2374 | 1.59375 | 56 | 9000 | 788 | 2374 | 2.234375 | 57 | 3000 | 5 | 26 | 0.125 | 57 | 6000 | 5 | 26 | 0.203125 | 57 | 9000 | 5 | 26 | 0.28125 | 58 | 3000 | 5 | 26 | 0.125 | 58 | 6000 | 5 | 26 | 0.21875 | 58 | 9000 | 5 | 26 | 0.34375 | 59 | 3000 | 5 | 26 | 0.125 | 59 | 6000 | 5 | 26 | 0.25 | 59 | 9000 | 5 | 26 | 0.234375 | 60 | 3000 | 5 | 26 | 0.125 | 60 | 6000 | 5 | 26 | 0.234375 | 60 | 9000 | 5 | 26 | 0.34375 | 61 | 3000 | 5 | 26 | 0.109375 | 61 | 6000 | 5 | 26 | 0.203125 | 61 | 9000 | 5 | 26 | 0.28125 | 62 | 3000 | 5 | 26 | 0.125 | 62 | 6000 | 5 | 26 | 0.25 | 62 | 9000 | 5 | 26 | 0.359375 | 63 | 3000 | 5 | 26 | 0.125 | 63 | 6000 | 5 | 26 | 0.25 | 63 | 9000 | 5 | 26 | 0.265625 | 64 | 3000 | 5 | 26 | 0.1875 | 64 | 6000 | 5 | 26 | 0.25 | 64 | 9000 | 5 | 26 | 0.25 | 65 | 3000 | 6 | 32 | 0.1875 | 65 | 6000 | 6 | 32 | 0.28125 | 65 | 9000 | 6 | 32 | 0.328125 | 66 | 3000 | 6 | 32 | 0.125 | 66 | 6000 | 6 | 32 | 0.1875 | 66 | 9000 | 6 | 32 | 0.234375 | 67 | 3000 | 22 | 99 | 0.125 | 67 | 6000 | 14 | 65 | 0.125 | 67 | 9000 | 21 | 95 | 0.234375 | 68 | 3000 | 11 | 62 | 0.0625 | 68 | 6000 | 11 | 62 | 0.0625 | 68 | 9000 | 11 | 62 | 0.0625 | 69 | 3000 | 6 | 32 | 0 | 69 | 6000 | 6 | 32 | 0.0625 | 69 | 9000 | 6 | 32 | 0.0625 | 70 | 3000 | 6 | 32 | 0.125 | 70 | 6000 | 6 | 32 | 0.203125 | 70 | 9000 | 6 | 32 | 0.375 | 71 | 3000 | 788 | 2374 | 0.8125 | 71 | 6000 | 788 | 2374 | 1.46875 | 71 | 9000 | 788 | 2374 | 2.265625 | 72 | 3000 | 88 | 390 | 5.984375 | 72 | 6000 | 91 | 406 | 19.34375 | 72 | 9000 | 92 | 415 | 42.32813 | 73 | 3000 | 83 | 357 | 0.125 | 73 | 6000 | 83 | 361 | 0.09375 | 73 | 9000 | 84 | 366 | 0.203125 | 74 | 3000 | 83 | 357 | 0.0625 | 74 | 6000 | 83 | 361 | 0.15625 | 74 | 9000 | 84 | 366 | 0.203125 |
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