强Wolfe线搜索下的修正PRP和HS共轭梯度法

马国栋

Improved PRP and HS Conjugate Gradient Methods with the Strong Wolfe Line Search

Guodong Ma

表 2 第二组方法数值试验报告

序号 算例 IHS VHS YWH IDY DY 算例名/维数 Itr/NF/NG/Tcpu/||gk|| Itr/NF/NG/Tcpu/||gk|| Itr/NF/NG/Tcpu/||gk|| Itr/NF/NG/Tcpu/||gk|| Itr/NF/NG/Tcpu/||gk|| 1 bdexp 10 3/1/3/0.001/2.25e-48 3/1/3/0.001/5.63e-49 3/1/3/0.001/5.63e-49 3/1/3/0.001/9.95e-49 3/1/3/0.000/8.27e-54 2 bdexp 100 3/2/3/0.001/1.33e-82 3/2/3/0.001/1.24e-82 3/2/3/0.001/1.24e-82 3/2/3/0.001/1.22e-82 3/2/3/0.001/2.02e-83 3 bdexp 1000 3/2/3/0.002/4.45e-107 3/2/3/0.001/4.45e-107 3/2/3/0.001/4.45e-107 3/2/3/0.001/4.40e-107 3/2/3/0.001/3.49e-107 4 bdexp 10000 3/2/3/0.012/1.14e-109 3/2/3/0.009/1.14e-109 3/2/3/0.006/1.14e-109 3/2/3/0.005/1.13e-109 3/2/3/0.005/1.11e-109 5 bdexp 20000 3/2/3/0.015/1.07e-109 3/2/3/0.017/1.07e-109 3/2/3/0.019/1.07e-109 3/2/3/0.020/1.07e-109 3/2/3/0.018/1.06e-109 6 exdenschnb 6 27/575/270/0.031/6.48e-07 46/1205/572/0.060/5.91e-06 85/2160/1080/0.102/9.61e-06 F/F/F/F/F 45/1082/500/0.049/2.80e-06 7 exdenschnb 8 27/575/270/0.035/7.48e-07 46/1205/581/0.070/6.83e-06 82/2086/1040/0.099/9.94e-06 F/F/F/F/F 45/1082/521/0.050/3.23e-06 8 himmelbg 200 3/6/7/0.001/7.14e-29 3/6/7/0.001/7.12e-29 3/6/7/0.001/7.12e-29 3/6/7/0.001/7.13e-29 3/6/7/0.001/6.93e-29 9 himmelbg 1000 3/6/7/0.001/1.60e-28 3/6/7/0.001/1.59e-28 3/6/7/0.001/1.59e-28 3/6/7/0.001/1.59e-28 3/6/7/0.001/1.55e-28 10 himmelbg 2000 3/6/7/0.001/2.26e-28 3/6/7/0.001/2.25e-28 3/6/7/0.001/2.25e-28 3/6/7/0.001/2.25e-28 3/6/7/0.001/2.19e-28 11 himmelbg 5000 3/6/7/0.003/3.57e-28 3/6/7/0.003/3.56e-28 3/6/7/0.003/3.56e-28 3/6/7/0.004/3.57e-28 3/6/7/0.004/3.47e-28 12 genquartic 200 21/337/151/0.021/2.29e-06 38/872/413/0.058/5.45e-06 92/2398/1194/0.124/6.62e-06 63/1571/737/0.087/3.97e-06 821/19378 /9592/1.049/9.80e-06 13 genquartic 500 30/599/289/0.033/5.23e-06 36/712/351/0.047/4.93e-06 65/1501/760/0.112/1.08e-06 78/1989/962/0.114/9.02e-06 645/17776/8774/1.104/9.29e-06 14 genquartic 1000 26/497/224/0.034/2.70e-06 32/582/258/0.038/4.41e-06 149/4040/1993/0.282/6.24e-06 F/F/F/F/F 918/25177/12373/1.652/9.83e-06 15 biggsb1 10 92/2354/1072/0.137/8.90e-06 99/2590/1194/0.130/4.88e-06 93/2353/1157/0.118/6.10e-06 F/F/F/F/F 300/7576/3703/0.363/9.64e-06 16 biggsb1 20 223/6267/2797/0.328/4.70e-06 231/6441/2952/0.310/9.38e-06 141/3413/1740/0.158/9.96e-06 F/F/F/F/F 585/15571/7647/0.817/6.94e-06 17 fletcbv3 10 1/1/1/0.000/5.97e-06 1/1/1/0.000/5.97e-06 1/1/1/0.000/5.97e-06 1/1/1/0.000/5.97e-06 1/1/1/0.000/5.97e-06 18 nonscomp 50 71/1796/850/0.118/6.23e-06 49/988/455/0.047/4.92e-06 F/F/F/F/F F/F/F/F/F F/F/F/F/F 19 dixmaana 1500 15/177/73/0.187/8.55e-06 13/184/61/0.156/5.51e-06 F/F/F/F/F 18/267/110/0.237/2.08e-06 25/423/187/0.394/2.57e-06 20 dixmaan b 1500 11/140/44/0.147/2.91e-06 11/140/53/0.128/2.90e-06 18/316/132/0.297/9.49e-06 10/117/35/0.097/7.97e-06 13/172/69/0.155/5.31e-07 21 dixmaanc 1500 20/324/142/0.330/1.63e-06 24/400/169/0.369/4.89e-07 F/F/F/F/F 29/579/278/0.526/2.10e-06 F/F/F/F/F 22 dixmaand 1500 20/303/137/0.316/9.11e-06 18/297/129/0.272/7.43e-06 59/1312/656/1.246/7.34e-06 F/F/F/F/F F/F/F/F/F 23 dixmaanf 1500 384/10668/4805/9.600/6.61e-06 328/8716/3884/7.877/6.86e-06 368/9331/4633/8.518/9.40e-06 F/F/F/F/F 569/13296/6208/12.037/9.45e-06 24 dixmaang 1500 462/12937/5721/11.405/6.91e-06 349/9644/4160/8.895/9.67e-06 251/6303/3170/5.904/7.43e-06 F/F/F/F/F F/F/F/F/F 25 dixmaanh 1500 340/8992/4020/8.074/9.24e-06 443/12355/5798/11.331/6.07e-06 253/6592/3315/6.061/9.63e-06 F/F/F/F/F 545/12688/6055/11.547/9.72e-06 26 dqdrtic 500 112/2969/1315/0.169/4.71e-06 808/24158/10585/1.257/6.11e-06 234/5935/2961/0.308/8.73e-06 F/F/F/F/F 332/7838/3899/0.402/8.00e-06 27 dqdrtic 1000 448/12853/5663/0.829/6.15e-06 677/20184/8818/1.191/7.38e-06 195/5120/2524/0.303/6.75e-06 F/F/F/F/F 356/9315/4555/0.572/9.28e-06 28 dqdrtic 5000 211/5452/2496/0.871/9.23e-06 786/23433/10290/3.794/7.65e-06 329/9479/4559/1.520/7.36e-06 F/F/F/F/F 355/9103/4407/1.442/9.96e-06 29 edensch 200 40/923/459/0.120/3.76e-06 37/773/344/0.090/3.17e-06 99/2586/1330/0.303/2.67e-06 F/F/F/F/F F/F/F/F/F 30 edensch 500 48/1121/538/0.261/5.01e-06 48/1121/507/0.250/9.24e-06 F/F/F/F/F F/F/F/F/F 646/14842/7011/3.463/9.95e-06 31 fletchcr 20 96/2510/1184/0.133/3.12e-06 122/3213/1517/0.168/4.57e-06 100/2485/1271/0.143/5.84e-06 F/F/F/F/F 720/19851/9712/0.967/9.81e-06 32 fletchcr 50 108/2811/1292/0.143/9.45e-06 111/2937/1382/0.131/8.33e-06 70/1702/811/0.104/1.88e-06 F/F/F/F/F 353/9180/4634/0.447/8.43e-06 33 genrose 40000 394/11155/4844/14.998/1.15e-06 484/13780/6083/18.593/9.07e-06 617/16168/8104/22.158/6.56e-06 F/F/F/F/F F/F/F/F/F 34 genrose 50000 239/6311/2783/10.298/6.13e-06 307/8594/3772/13.857/3.30e-06 726/18954/9375/33.155/4.74e-06 F/F/F/F/F F/F/F/F/F 35 liarwhd 10 75/1884/846/0.104/7.13e-06 92/2380/1068/0.121/9.74e-06 81/1932/948/0.098/1.58e-06 F/F/F/F/F 169/4333/2143/0.236/7.07e-06 36 liarwhd 20 91/2350/1048/0.123/1.68e-06 147/3927/1783/0.204/4.36e-06 71/1791/870/0.101/1.15e-06 F/F/F/F/F 158/3925/1941/0.244/2.74e-06 37 penalt y1 1000 14/243/93/0.791/2.34e-06 14/243/93/0.758/2.34e-06 19/406/179/1.333/9.37e-07 19/406/177/1.367/9.37e-07 14/243/93/0.750/2.34e-06 38 penalt y1 2000 10/129/39/1.354/5.53e-06 10/129/39/1.301/5.53e-06 18/385/157/4.370/3.61e-08 18/385/157/4.268/3.61e-08 10/129/39/1.302/5.53e-06 39 penalt y1 5000 11/152/50/11.744/3.01e-06 11/152/50/11.720/3.01e-06 10/156/50/12.004/4.03e-06 10/156/50/11.701/4.03e-06 11/152/51/11.610/3.01e-06 40 quartc 20 12/131/50/0.012/1.48e-06 15/193/77/0.013/6.78e-07 25/465/214/0.027/7.65e-06 27/554/243/0.031/4.83e-06 42/907/438/0.049/8.77e-06 41 quartc 100 21/268/112/0.034/2.55e-06 22/298/107/0.042/5.43e-06 F/F/F/F/F 40/835/412/0.077/7.91e-06 F/F/F/F/F 42 tridia 10 93/2351/1061/0.138/6.02e-06 160/4450/1973/0.215/5.81e-06 143/3824/1885/0.193/6.63e-06 F/F/F/F/F 509/13202/6489/0.659/6.52e-06 43 tridia 30 243/6517/2942/0.339/7.01e-06 244/6428/2942/0.362/8.75e-06 229/6007/2989/0.310/9.35e-06 F/F/F/F/F F/F/F/F/F 44 raydan 1 50 54/1229/560/0.067/4.85e-06 65/1361/679/0.071/1.69e-06 91/2358/1158/0.114/5.16e-06 F/F/F/F/F 685/15740/7582/0.776/9.90e-06 45 raydan 1 80 69/1547/712/0.072/8.33e-06 98/2546/1222/0.123/8.71e-06 107/2819/1366/0.139/2.74e-06 F/F/F/F/F 602/13450/6380/0.789/9.59e-06 46 raydan2 1000 11/173/64/0.018/6.93e-06 11/173/66/0.014/6.95e-06 11/173/65/0.014/6.93e-06 11/173/65/0.014/6.95e-06 11/173/65/0.027/6.95e-06 47 raydan2 4000 12/204/79/0.055/9.01e-06 13/235/109/0.062/4.97e-06 15/268/96/0.063/4.95e-07 16/301/98/0.067/1.75e-06 15/271/92/0.079/7.57e-07 48 raydan2 10000 13/208/79/0.135/6.37e-09 14/236/90/0.139/2.02e-06 14/238/92/0.155/5.95e-07 15/272/115/0.157/1.62e-06 12/204/72/0.126/8.83e-06 49 diagonal 1 50 156/4632/2239/0.252/5.98e-06 168/5006/2447/0.314/9.21e-06 106/2632/1279/0.134/5.76e-06 F/F/F/F/F F/F/F/F/F 50 diagonal2 200 168/4488/2112/0.294/6.79e-06 232/6717/3155/0.423/5.53e-06 156/3915/1904/0.264/3.42e-06 F/F/F/F/F 901/23693/11745/1.642/9.54e-06 51 diagonal2 800 468/13834/6665/1.469/9.51e-06 460/13514/6589/1.395/4.10e-06 297/8009/3930/0.846/7.15e-06 F/F/F/F/F F/F/F/F/F 52 diagonal 3 5 82/2438/1160/0.146/4.57e-06 82/2438/1151/0.130/4.58e-06 90/2387/1194/0.115/7.49e-06 74/1924/927/0.106/6.19e-06 322/8250 /4083/0.460/9.78e-06 53 diagonal 3 20 107/3017/1401/0.150/8.29e-06 117/3398/1613/0.174/7.60e-06 91/2344/1142/0.131/8.12e-06 F/F/F/F/F 542/13718/6653/0.701/9.80e-06 54 bv 1000 1/1/1/0.000/4.99e-06 1/1/1/0.000/4.99e-06 1/1/1/0.000/4.99e-06 1/1/1/0.000/4.99e-06 1/1/1/0.000/4.99e-06 55 bv 10000 1/1/1/0.000/5.00e-08 1/1/1/0.000/5.00e-08 1/1/1/0.000/5.00e-08 1/1/1/0.000/5.00e-08 1/1/1/0.000/5.00e-08 56 ie 100 12/193/85/0.894/9.38e-06 11/166/75/0.729/2.85e-06 70/1873/917/8.274/4.81e-06 F/F/F/F/F 71/1838/904/7.827/9.92e-06 57 ie 200 14/225/89/3.598/2.89e-06 11/166/67/2.651/4.02e-06 102/2876/1443/48.512/3.88e-06 15/207/104/3.495/2.82e-06 62/1551/711/25.058/5.32e-06 58 singx 10 174/4588/2004/0.307/2.52e-06 618/18316/7284/1.186/8.99e-06 334/8361/4166/0.620/7.59e-06 F/F/F/F/F 731/19522/9716/1.219/9.55e-06 59 singx 150 175/4802/2117/0.758/6.53e-06 720/21252/8241/3.513/9.69e-06 601/15530/7775/2.721/3.25e-06 F/F/F/F/F 228/5911/2866/1.009/4.27e-06 60 beale 2 134/3736/1642/0.201/7.28e-06 203/5839/2717/0.305/3.43e-06 F/F/F/F/F F/F/F/F/F F/F/F/F/F 61 froth 2 933/26993/11996/1.634/9.76e-06 F/F/F/F/F F/F/F/F/F F/F/F/F/F 210/6330/3026/0.396/9.06e-06 62 lin 100 2/2/2/0.007/3.13e-14 2/2/2/0.004/3.13e-14 2/2/2/0.003/3.13e-14 2/2/2/0.002/3.13e-14 2/2/2/0.002/3.13e-14 63 lin 500 2/2/2/0.027/9.93e-14 2/2/2/0.019/9.93e-14 2/2/2/0.019/9.93e-14 2/2/2/0.016/9.93e-14 2/2/2/0.024/9.93e-14 64 trid 120 963/28247/12176/6.211/6.81e-06 F/F/F/F/F 461/11845/5899/2.515/6.45e-06 F/F/F/F/F F/F/F/F/F