Research Article
Modified Three-Term Liu–Storey Conjugate Gradient Method for Solving Unconstrained Optimization Problems and Image Restoration Problems
Table 1
Test results of the TTMLS algorithm.
| Nr | Dim | TTMLS algorithm | NI | NFG | CPU |
| 1 | 3000 | 5 | 26 | 0.203125 | 1 | 6000 | 5 | 26 | 0.109375 | 1 | 9000 | 5 | 26 | 0.234375 | 2 | 3000 | 85 | 402 | 3.640625 | 2 | 6000 | 90 | 426 | 6.171875 | 2 | 9000 | 91 | 434 | 9.125 | 3 | 3000 | 6 | 32 | 0.0625 | 3 | 6000 | 6 | 32 | 0.0625 | 3 | 9000 | 6 | 32 | 0.046875 | 4 | 3000 | 5 | 26 | 0.0625 | 4 | 6000 | 5 | 26 | 0.15625 | 4 | 9000 | 5 | 26 | 0.171875 | 5 | 3000 | 5 | 26 | 0.015625 | 5 | 6000 | 5 | 26 | 0.046875 | 5 | 9000 | 5 | 26 | 0.0625 | 6 | 3000 | 4 | 20 | 0.0625 | 6 | 6000 | 4 | 20 | 0.0625 | 6 | 9000 | 4 | 20 | 0.0625 | 7 | 3000 | 78 | 342 | 0.140625 | 7 | 6000 | 80 | 353 | 0.234375 | 7 | 9000 | 80 | 354 | 0.328125 | 8 | 3000 | 10 | 40 | 0.03125 | 8 | 6000 | 10 | 40 | 0.0625 | 8 | 9000 | 10 | 40 | 0.0625 | 9 | 3000 | 6 | 20 | 0 | 9 | 6000 | 6 | 20 | 0.0625 | 9 | 9000 | 6 | 20 | 0 | 10 | 3000 | 3 | 14 | 0.0625 | 10 | 6000 | 3 | 14 | 0.0625 | 10 | 9000 | 3 | 14 | 0.0625 | 11 | 3000 | 1000 | 2999 | 2.359375 | 11 | 6000 | 1000 | 2999 | 4.625 | 11 | 9000 | 1000 | 2999 | 6.859375 | 12 | 3000 | 3 | 14 | 0.0625 | 12 | 6000 | 3 | 14 | 0.0625 | 12 | 9000 | 3 | 14 | 0.0625 | 13 | 3000 | 4 | 17 | 0 | 13 | 6000 | 4 | 17 | 0.0625 | 13 | 9000 | 4 | 20 | 0.109375 | 14 | 3000 | 7 | 38 | 0.25 | 14 | 6000 | 7 | 38 | 0.375 | 14 | 9000 | 7 | 38 | 0.46875 | 15 | 3000 | 7 | 38 | 0.1875 | 15 | 6000 | 7 | 38 | 0.265625 | 15 | 9000 | 7 | 38 | 0.390625 | 16 | 3000 | 4 | 20 | 0 | 16 | 6000 | 4 | 20 | 0.046875 | 16 | 9000 | 4 | 20 | 0.0625 | 17 | 3000 | 5 | 26 | 0.125 | 17 | 6000 | 5 | 26 | 0.140625 | 17 | 9000 | 5 | 26 | 0.25 | 18 | 3000 | 1000 | 3073 | 0.8125 | 18 | 6000 | 1000 | 3073 | 1.421875 | 18 | 9000 | 1000 | 3073 | 1.984375 | 19 | 3000 | 10 | 29 | 0.0625 | 19 | 6000 | 10 | 29 | 0.0625 | 19 | 9000 | 10 | 29 | 0.125 | 20 | 3000 | 7 | 38 | 0.0625 | 20 | 6000 | 7 | 38 | 0.0625 | 20 | 9000 | 7 | 38 | 0.109375 | 21 | 3000 | 6 | 32 | 0.1875 | 21 | 6000 | 6 | 32 | 0.265625 | 21 | 9000 | 6 | 32 | 0.34375 | 22 | 3000 | 9 | 50 | 0.15625 | 22 | 6000 | 9 | 50 | 0.25 | 22 | 9000 | 9 | 50 | 0.390625 | 23 | 3000 | 6 | 32 | 0.125 | 23 | 6000 | 6 | 32 | 0.125 | 23 | 9000 | 6 | 32 | 0.171875 | 24 | 3000 | 232 | 714 | 0.4375 | 24 | 6000 | 243 | 747 | 0.890625 | 24 | 9000 | 249 | 765 | 1.296875 | 25 | 3000 | 6 | 32 | 0.0625 | 25 | 6000 | 6 | 32 | 0.0625 | 25 | 9000 | 6 | 32 | 0.0625 | 26 | 3000 | 4 | 14 | 0 | 26 | 6000 | 4 | 14 | 0 | 26 | 9000 | 4 | 14 | 0.0625 | 27 | 3000 | 79 | 346 | 0.125 | 27 | 6000 | 80 | 353 | 0.234375 | 27 | 9000 | 81 | 358 | 0.28125 | 28 | 3000 | 5 | 26 | 0 | 28 | 6000 | 5 | 26 | 0 | 28 | 9000 | 5 | 26 | 0.046875 | 29 | 3000 | 7 | 38 | 0.015625 | 29 | 6000 | 7 | 38 | 0.0625 | 29 | 9000 | 7 | 38 | 0.0625 | 30 | 3000 | 76 | 333 | 0.0625 | 30 | 6000 | 78 | 342 | 0.171875 | 30 | 9000 | 78 | 344 | 0.203125 | 31 | 3000 | 5 | 26 | 0.03125 | 31 | 6000 | 5 | 26 | 0 | 31 | 9000 | 5 | 26 | 0.0625 | 32 | 3000 | 5 | 26 | 0.125 | 32 | 6000 | 5 | 26 | 0.1875 | 32 | 9000 | 5 | 26 | 0.1875 | 33 | 3000 | 6 | 32 | 0 | 33 | 6000 | 6 | 32 | 0 | 33 | 9000 | 6 | 32 | 0.0625 | 34 | 3000 | 5 | 26 | 0.0625 | 34 | 6000 | 5 | 26 | 0.0625 | 34 | 9000 | 5 | 26 | 0.046875 | 35 | 3000 | 6 | 28 | 0 | 35 | 6000 | 6 | 28 | 0 | 35 | 9000 | 6 | 28 | 0 | 36 | 3000 | 5 | 26 | 0.078125 | 36 | 6000 | 5 | 26 | 0.125 | 36 | 9000 | 5 | 26 | 0.21875 | 37 | 3000 | 82 | 366 | 0.078125 | 37 | 6000 | 84 | 378 | 0.140625 | 37 | 9000 | 85 | 382 | 0.34375 | 38 | 3000 | 5 | 26 | 0 | 38 | 6000 | 5 | 26 | 0 | 38 | 9000 | 5 | 26 | 0.0625 | 39 | 3000 | 5 | 26 | 0.0625 | 39 | 6000 | 5 | 26 | 0.0625 | 39 | 9000 | 5 | 26 | 0.0625 | 40 | 3000 | 5 | 26 | 0.125 | 40 | 6000 | 5 | 26 | 0.15625 | 40 | 9000 | 5 | 26 | 0.25 | 41 | 3000 | 73 | 312 | 0.0625 | 41 | 6000 | 73 | 312 | 0.140625 | 41 | 9000 | 73 | 312 | 0.265625 | 42 | 3000 | 37 | 204 | 0.1875 | 42 | 6000 | 30 | 170 | 0.296875 | 42 | 9000 | 43 | 238 | 0.59375 | 43 | 3000 | 5 | 26 | 0.140625 | 43 | 6000 | 5 | 26 | 0.25 | 43 | 9000 | 5 | 26 | 0.359375 | 44 | 3000 | 5 | 26 | 0.1875 | 44 | 6000 | 5 | 26 | 0.25 | 44 | 9000 | 5 | 26 | 0.265625 | 45 | 3000 | 5 | 26 | 0.140625 | 45 | 6000 | 5 | 26 | 0.21875 | 45 | 9000 | 5 | 26 | 0.265625 | 46 | 3000 | 5 | 26 | 0.125 | 46 | 6000 | 5 | 26 | 0.25 | 46 | 9000 | 5 | 26 | 0.28125 | 47 | 3000 | 82 | 368 | 3.9375 | 47 | 6000 | 85 | 386 | 11.29688 | 47 | 9000 | 87 | 396 | 23.98438 | 48 | 3000 | 6 | 32 | 0.1875 | 48 | 6000 | 6 | 32 | 0.171875 | 48 | 9000 | 6 | 32 | 0.3125 | 49 | 3000 | 78 | 342 | 0.0625 | 49 | 6000 | 80 | 353 | 0.1875 | 49 | 9000 | 80 | 354 | 0.296875 | 50 | 3000 | 78 | 342 | 0.9375 | 50 | 6000 | 80 | 353 | 1.8125 | 50 | 9000 | 80 | 354 | 2.234375 | 51 | 3000 | 7 | 38 | 0.125 | 51 | 6000 | 7 | 38 | 0.28125 | 51 | 9000 | 7 | 38 | 0.375 | 52 | 3000 | 4 | 20 | 0.0625 | 52 | 6000 | 4 | 20 | 0.125 | 52 | 9000 | 4 | 20 | 0.0625 | 53 | 3000 | 1000 | 3032 | 0.875 | 53 | 6000 | 1000 | 3032 | 1.609375 | 53 | 9000 | 1000 | 3033 | 2.4375 | 54 | 3000 | 5 | 26 | 0 | 54 | 6000 | 5 | 26 | 0 | 54 | 9000 | 5 | 26 | 0.046875 | 55 | 3000 | 24 | 74 | 0.109375 | 55 | 6000 | 26 | 80 | 0.375 | 55 | 9000 | 26 | 80 | 0.5 | 56 | 3000 | 1000 | 3010 | 0.90625 | 56 | 6000 | 1000 | 3010 | 1.6875 | 56 | 9000 | 1000 | 3010 | 2.46875 | 57 | 3000 | 5 | 26 | 0.125 | 57 | 6000 | 5 | 26 | 0.21875 | 57 | 9000 | 5 | 26 | 0.265625 | 58 | 3000 | 5 | 26 | 0.125 | 58 | 6000 | 5 | 26 | 0.21875 | 58 | 9000 | 5 | 26 | 0.25 | 59 | 3000 | 5 | 26 | 0.125 | 59 | 6000 | 5 | 26 | 0.234375 | 59 | 9000 | 5 | 26 | 0.28125 | 60 | 3000 | 5 | 26 | 0.125 | 60 | 6000 | 5 | 26 | 0.25 | 60 | 9000 | 5 | 26 | 0.28125 | 61 | 3000 | 5 | 26 | 0.1875 | 61 | 6000 | 5 | 26 | 0.25 | 61 | 9000 | 5 | 26 | 0.3125 | 62 | 3000 | 5 | 26 | 0.1875 | 62 | 6000 | 5 | 26 | 0.25 | 62 | 9000 | 5 | 26 | 0.359375 | 63 | 3000 | 5 | 26 | 0.1875 | 63 | 6000 | 5 | 26 | 0.25 | 63 | 9000 | 5 | 26 | 0.3125 | 64 | 3000 | 5 | 26 | 0.140625 | 64 | 6000 | 5 | 26 | 0.25 | 64 | 9000 | 5 | 26 | 0.28125 | 65 | 3000 | 6 | 32 | 0.203125 | 65 | 6000 | 6 | 32 | 0.3125 | 65 | 9000 | 6 | 32 | 0.28125 | 66 | 3000 | 6 | 32 | 0.078125 | 66 | 6000 | 6 | 32 | 0.1875 | 66 | 9000 | 6 | 32 | 0.25 | 67 | 3000 | 12 | 61 | 0.0625 | 67 | 6000 | 14 | 74 | 0.09375 | 67 | 9000 | 13 | 69 | 0.1875 | 68 | 3000 | 11 | 62 | 0.0625 | 68 | 6000 | 11 | 62 | 0.0625 | 68 | 9000 | 11 | 62 | 0.0625 | 69 | 3000 | 6 | 32 | 0.03125 | 69 | 6000 | 6 | 32 | 0.0625 | 69 | 9000 | 6 | 32 | 0.0625 | 70 | 3000 | 6 | 32 | 0.1875 | 70 | 6000 | 6 | 32 | 0.25 | 70 | 9000 | 6 | 32 | 0.34375 | 71 | 3000 | 1000 | 3010 | 1.015625 | 71 | 6000 | 1000 | 3010 | 1.8125 | 71 | 9000 | 1000 | 3010 | 2.59375 | 72 | 3000 | 82 | 368 | 4.1875 | 72 | 6000 | 86 | 389 | 11.51563 | 72 | 9000 | 87 | 396 | 23.92188 | 73 | 3000 | 76 | 333 | 0.09375 | 73 | 6000 | 78 | 342 | 0.15625 | 73 | 9000 | 78 | 344 | 0.234375 | 74 | 3000 | 76 | 333 | 0.0625 | 74 | 6000 | 78 | 342 | 0.125 | 74 | 9000 | 78 | 344 | 0.21875 |
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