Table 2.

Numerical results for the three tested methods (continued).

Problems	hHPR	DHS	DPRP
TP/Dim	Itr/Tcpu/‖g∗‖	Itr/Tcpu/‖g∗‖	Itr/Tcpu/‖g∗‖
liarwhd/5000	94/0.066/7.37e − 07	—	—
liarwhd/10000	138/0.186/8.02e − 07	—	—
liarwhd/20000	125/0.388/7.88e − 07	—	—
nondquar/30	534/0.072/8.10e − 07	760/0.085/9.19e − 07	—
penalty1/1000	30/0.418/2.55e − 07	29/0.411/2.65e − 07	29/0.390/9.90e − 07
penalty1/5000	117/39.785/2.62e − 07	278/103.383/4.27e − 07	203/72.649/1.01e − 07
power1/50	595/0.029/9.03e − 07	743/0.039/9.46e − 07	917/0.050/2.82e − 07
power1/100	1468/0.068/9.91e − 07	1666/0.101/6.89e − 07	—
quartc/100	23/0.010/6.45e − 08	21/0.004/3.28e − 07	27/0.006/1.06e − 07
quartc/560	32/0.023/7.15e − 07	29/0.020/7.08e − 07	33/0.022/5.70e − 07
tridia/100	409/0.026/6.30e − 07	477/0.030/3.94e − 07	681/0.038/9.21e − 07
tridia/1000	1564/0.153/9.39e − 07	—	—
raydan1/100	77/0.008/9.73e − 07	127/0.010/8.52e − 07	106/0.005/9.59e − 07
raydan1/500	210/0.015/9.14e − 07	281/0.023/5.80e − 07	268/0.022/7.43e − 07
raydan2/5000	12/0.027/9.72e − 07	12/0.021/3.54e − 07	12/0.023/3.54e − 07
raydan2/10000	12/0.051/3.75e − 07	13/0.052/7.31e − 08	13/0.050/7.31e − 08
raydan2/50000	16/0.239/2.43e − 08	16/0.217/8.05e − 07	17/0.272/7.70e − 07
diagonal1/40	61/0.010/7.58e − 07	81/0.005/7.52e − 07	63/0.004/8.67e − 07
diagonal2/10000	830/1.082/9.48e − 07	1398/2.017/9.75e − 07	1134/1.660/6.18e − 07
diagonal2/20000	1241/3.050/8.03e − 07	1387/4.025/9.98e − 07	1879/5.192/8.08e − 07
diagonal3/10	39/0.007/7.69e − 07	37/0.002/4.92e − 07	39/0.002/4.59e − 07
diagonal3/90	91/0.008/7.31e − 07	144/0.010/9.04e − 07	166/0.016/6.14e − 07
bv/1000	138/0.447/8.56e − 07	117/0.513/8.14e − 07	127/0.550/9.09e − 07
bv/2000	105/1.174/9.03e − 07	107/1.476/8.99e − 07	130/1.701/9.46e − 07
ie/50	16/0.051/9.24e − 07	11/0.039/2.20e − 07	15/0.044/1.83e − 07
ie/10	14/0.162/7.41e − 07	12/0.156/2.72e − 07	13/0.167/2.10e − 07
singx/100	277/0.051/3.49e − 07	—	—
singx/1000	565/2.397/7.35e − 07	—	453/1.711/5.18e − 07
woods/10000	177/0.175/2.74e − 07	589/0.492/2.25e − 07	814/0.631/8.15e − 07
band/3	19/0.012/2.13e − 07	15/0.002/6.71e − 07	18/0.002/9.14e − 07
bard/3	101/0.028/3.00e − 07	698/0.097/4.95e − 07	811/0.112/8.16e − 07
beale/2	48/0.010/6.38e − 07	131/0.007/2.30e − 07	96/0.007/8.34e − 07
biggs/6	—	—	—
box/3	74/0.014/5.48e − 07	203/0.017/1.45e − 07	185/0.015/5.45e − 07
froth/2	92/0.014/6.85e − 07	338/0.025/9.02e − 07	381/0.026/8.13e − 07
gauss/3	13/0.010/3.75e − 07	24/0.004/4.71e − 07	21/0.003/3.27e − 07
helix/3	102/0.019/4.65e − 07	361/0.032/9.10e − 07	418/0.036/9.20e − 07
jensam/2	39/0.009/2.79e − 07	148/0.009/9.70e − 07	149/0.009/8.40e − 07
kowosb/4	224/0.029/9.98e − 07	1029/0.075/3.25e − 07	797/0.056/9.64e − 07
lin/100	13/0.062/8.86e − 07	13/0.054/8.86e − 07	13/0.054/8.86e − 07
lin/500	18/0.418/9.57e − 07	18/0.420/9.38e − 07	18/0.421/9.38e − 07
osb2/11	734/0.113/7.42e − 07	1513/0.259/4.38e − 07	1174/0.198/7.47e − 07
pen1/60	78/0.025/4.74e − 07	390/0.056/8.20e − 07	668/0.079/8.95e − 07
pen2/100	151/0.074/7.94e − 07	162/0.045/5.89e − 07	235/0.081/8.49e − 07
rose/2	79/0.011/9.71e − 07	584/0.037/9.06e − 07	858/0.053/2.86e − 07
rosex/100	104/0.022/4.68e − 07	1190/0.132/7.73e − 07	705/0.080/8.08e − 07
rosex/1000	106/0.899/2.49e − 07	1040/6.318/8.60e − 07	1374/8.180/2.95e − 07
sing/4	213/0.023/6.12e − 07	—	1111/0.070/9.15e − 07
trid/100	80/0.021/4.41e − 07	112/0.022/4.22e − 07	128/0.024/6.31e − 07
trid/200	37/0.015/6.81e − 07	46/0.016/7.20e − 07	42/0.017/6.19e − 07
vardim/8	28/0.011/4.13e − 07	26/0.004/6.51e − 07	31/0.004/9.75e − 07
watson/6	1811/0.500/7.74e − 07	—	—
wood/4	173/0.020/6.93e − 07	622/0.047/5.42e − 07	966/0.069/9.26e − 07