列正交约束下广义Sylvester方程极小化问题的有效算法
刘月园,王凯,秦树娟,李姣芬

An Effective Algorithm for Generalized Sylvester Equation Minimization Problem Under Columnwise Orthogonal Constraints
Yueyuan Liu,Kai Wang,Shujuan Qin,Jiaofen Li
表 1 算法1与其它几类算法的数值比较结果
l, n, p, s CPU(s) IT ||grad f(Xk)|| f(Xk) Xfeasi
Algo.1 0.134 183 7.202×10-4 0 9.744×10-16
OptStiefel 0.282 246 9.431×10-4 0 4.220×10-15
Mixed 15, 200, 10, 5 0.532 568 8.770×10-4 0 2.048×10-15
SOC 3.775 196 9.278×10-4 0 3.593×10-2
ADM 3.485 49 9.823×10-4 0 5.866×10-2
Major 11.784 20000 6.235×10-2 0.0003 5.209×10-15
Algo.1 0.205 170 7.973×10-4 0 1.324×10-15
OptStiefel 0.904 271 5.123×10-4 0 1.832×10-14
Mixed 30, 300, 15, 5 1.524 956 9.914×10-4 0 2.808×10-15
SOC 15.229 219 9.536×10-4 0 3.578×10-2
ADM 14.663 206 9.741×10-4 0 3.356×10-2
Major 32.982 20000 3.500×10-1 0.0018 6.742×10-15
Algo.1 0.673 486 5.942×10-4 0 1.595×10-15
OptStiefel 1.154 356 5.515×10-4 0 1.449×10-15
Mixed 45, 400, 20, 5 4.586 1393 8.224×10-4 0 4.064×10-15
SOC 54.639 116 9.679×10-4 0 5.821×10-2
ADM 31.334 37 9.979×10-4 0 1.635×10-1
Major 114.029 20000 4.797 0.2222 8.883×10-15
Algo.1 0.647 293 4.311×10-4 0 1.277×10-15
OptStiefel 1.216 364 9.407×10-4 0 1.277×10-15
Mixed 50, 500, 20, 5 5.546 1156 7.179×10-4 0 3.165×10-15
SOC 72.800 51 8.914×10-4 0 1.201×10-1
ADM 72.570 46 8.835×10-4 0 1.313×10-1
Major 185.344 20000 2.804 0.0429 7.434×10-15
Algo.1 0.609 239 5.557×10-1 0.0001 2.313×10-15
OptStiefel 1.125 398 1.635×10-2 0 1.524×10-15
Mixed 60, 400, 30, 5 9.036 2072 1.069×10-3 0 4.994×10-15
SOC 88.718 56 9.967×10-4 0 9.761×10-2
ADM 105.745 99 9.206×10-4 0 1.023×10-1
Major 217.668 20000 1.224×101 0.7462 9.998×10-15
Algo.1 1.866 636 7.307×10-4 0 1.272×10-15
OptStiefel 1.846 518 9.739×10-4 0 8.997×10-16
Mixed 70, 500, 15, 5 8.198 1966 5.506×10-4 0 2.639×10-15
SOC 58.076 97 8.202×10-4 0 1.162×10-1
ADM 57.401 83 9.283×10-4 0 1.065×10-1
Major 130.671 20000 7.300 0.4279 5.167×10-15
Algo.1 1.289 645 5.152×10-4 0 1.798×10-15
OptStiefel 1.985 669 9.542×10-4 0 1.287×10-15
Mixed 80, 500, 20, 5 11.044 2311 8.951×10-4 0 3.750×10-15
SOC 126.369 92 8.061×10-4 0 2.926×10-1
ADM 186.829 198 8.944×10-4 0 7.416×10-2
Major 183.599 20000 1.009×101 0.5858 7.192×10-15