Research Article
Effective Algorithms for Solving Trace Minimization Problem in Multivariate Statistics
Table 5
Comparison results of the considered algorithms.
| | CT. | IT. | Grad. | Obj. |
| | Algorithm 2 | 0.04 | 127/2 | 6.49 × | −73.76 | Algorithm 3 | 0.35 | 127/3 | 6.41 × | −73.76 | Existing-RTR | 0.44 | 16 | 1.28 × | −73.76 | Existing-RBFGS | 0.87 | 281 | 8.93 × | −73.76 | OptStiefel | 0.04 | 270 | 1.27 × | −73.76 | RCG-Cayley | 0.11 | 446 | 1.83 × | −73.76 | RCG-Pol | 0.84 | 2000 | 7.87 × | −73.75 | RCG-QR | 0.07 | 369 | 1.20 × | −73.76 | RGPRP-CG | 0.04 | 233 | 1.45 × | −73.76 | RFR-CG | 0.29 | 2000 | 1.32 × | −73.76 |
| | Algorithm 2 | 0.19 | 140/4 | 9.86 × | −76.97 | Algorithm 3 | 0.63 | 140/5 | 5.89 × | −76.97 | Existing-RTR | 0.57 | 15 | 2.95e − 10 | −76.97 | Existing-RBFGS | 1.31 | 387 | 8.63 × | −76.97 | OptStiefel | 0.19 | 501 | 1.26 × | −76.97 | RCG-Cayley | 0.60 | 985 | 2.05 × | −76.97 | RCG-Pol | 2.99 | 2000 | 1.64 × | −76.95 | RCG-QR | 0.43 | 696 | 6.43 × | −76.97 | RGPRP-CG | 0.15 | 353 | 1.32 × | −76.97 | RFR-CG | 0.93 | 2000 | 3.93 × | −76.87 |
| | Algorithm 2 | 1.74 | 258/4 | 5.72 × | −79.90 | Algorithm 3 | 1.15 | 258/5 | 7.54 × | −79.90 | Existing-RTR | 0.82 | 18 | 3.29 × | −79.90 | Existing-RBFGS | 2.96 | 676 | 8.33 × | −79.90 | OptStiefel | 0.57 | 648 | 1.11 × | −79.90 | RCG-Cayley | 1.45 | 1038 | 7.97 × | −79.90 | RCG-Pol | 5.70 | 1604 | 7.51 × | −79.87 | RCG-QR | 1.33 | 965 | 3.60 × | −79.90 | RGPRP-CG | 0.49 | 511 | 1.46 × | −79.90 | RFR-CG | 1.99 | 2000 | 5.32 × | −79.90 |
| | Algorithm 2 | 4.60 | 157/4 | 5.25 × | −81.55 | Algorithm 3 | 1.55 | 157/5 | 9.16 × | −81.55 | Existing-RTR | 1.06 | 15 | 4.85 × | −81.55 | Existing-RBFGS | 3.58 | 650 | 8.95 × | −81.55 | OptStiefel | 1.77 | 992 | 1.36 × | −81.55 | RCG-Cayley | 2.09 | 749 | 2.03 × | −81.55 | RCG-Pol | 15.14 | 2000 | 1.55 × | −81.54 | RCG-QR | 1.95 | 703 | 1.34 × | −81.55 | RGPRP-CG | 0.83 | 426 | 1.51 × | −81.55 | RFR-CG | 3.87 | 2000 | 1.74 × | −81.48 |
| | Algorithm 2 | 21.52 | 135/13 | 5.83 × | −82.68 | Algorithm 3 | 2.59 | 135/5 | 4.53 × | −82.69 | Existing-RTR | 1.41 | 17 | 3.07 × | −82.69 | Existing-RBFGS | 8.27 | 703 | 9.69 × | −82.69 | OptStiefel | 3.41 | 529 | 2.76 × | −82.69 | RCG-Cayley | 8.21 | 787 | 1.61 × | −82.69 | RCG-Pol | 58.01 | 2000 | 6.95 × | −82.67 | RCG-QR | 14.58 | 1420 | 1.15 × | −82.69 | RGPRP-CG | 4.19 | 626 | 1.64 × | −82.69 | RFR-CG | 15.72 | 2000 | 1.63 × | −82.65 |
| | Algorithm 2 | 28.07 | 138/12 | 5.12 × | −83.55 | Algorithm 3 | 5.40 | 138/8 | 2.87 × | −83.55 | Existing-RTR | 4.09 | 19 | 3.37 × | −83.55 | Existing-RBFGS | 15.39 | 917 | 1.00 × | −83.55 | OptStiefel | 13.00 | 1317 | 1.66 × | −83.55 | RCG-Cayley | 29.72 | 1829 | 2.70 × | −83.55 | RCG-Pol | 82.85 | 1838 | 3.66 × | −83.54 | RCG-QR | 24.98 | 1569 | 4.00 × | −83.55 | RGPRP-CG | 11.26 | 1051 | 1.22 × | −83.55 | RFR-CG | 21.09 | 2000 | 1.88 × | −83.48 | | Algorithm 2 | 56.49 | 147/14 | 8.44 × | −84.25 | Algorithm 3 | 6.28 | 147/9 | 4.36 × | −84.25 | Existing-RTR | 2.97 | 20 | 9.91 × | −84.25 | Existing-RBFGS | 16.56 | 800 | 9.75 × | −84.25 | OptStiefel | 20.03 | 1436 | 1.28 × | −84.25 | RCG-Cayley | 32.21 | 1427 | 2.60 × | −84.25 | RCG-Pol | 125.53 | 2000 | 3.98 × | −84.24 | RCG-QR | 24.08 | 1067 | 2.53 × | −84.25 | RGPRP-CG | 17.47 | 1150 | 1.47 × | −84.25 | RFR-CG | 30.46 | 2000 | 4.96 × | −84.12 |
| | Algorithm 2 | 67.50 | 143/11 | 4.94 × | −84.83 | Algorithm 3 | 5.08 | 143/6 | 9.72 × | −84.84 | Existing-RTR | 3.36 | 17 | 3.83 × | −84.84 | Existing-RBFGS | 16.68 | 609 | 1.04 × | −84.84 | OptStiefel | 13.63 | 720 | 1.22 × | −84.84 | RCG-Cayley | 25.07 | 839 | 1.57 × | −84.84 | RCG-Pol | 171.96 | 2000 | 1.53 × | −84.82 | RCG-QR | 22.82 | 793 | 4.87 × | −84.84 | RGPRP-CG | 14.48 | 717 | 1.35 × | −84.84 | RFR-CG | 41.21 | 2000 | 9.98 × | −84.81 |
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