New Investigation for the Liu-Story Scaled Conjugate Gradient Method for Nonlinear Optimization

Table 2

Comparisons of new algorithm against (HS) & (PR) algorithms for the total of (60) test problems with (1000  n  10000, and the increasing size in n is equal to 1000) with (c = 0.1 and 0.001).

Prob.	New algorithm (C = 0.1) NOI/NOFG/TIME	New algorithm (C = 0.001) NOI/NOFG/TIME	HS; NOI/NOFG/TIME	PR; NOI/NOFG/TIME
1	99/252/0.14	101/263/0.14	5902/173484/0.72	11798/270815/6.07
2	408/884/2.02	405/880/1.97	362/637/1.83	416/720/2.07
3	853/2183/1.06	830/2171/0.98	789/1817/0.86	989/1979/1.11
4	123/308/0.14	123/308/0.15	141/281/0.19	254/430/0.26
5	100/388/0.15	100/388/0.20	653/17073/3.79	410/7948/2.73
6	585/995/1.56	585/995/1.54	9881/16243/3.07	20010/22091/4.04
7	30/80/0.15	30/80/0.13	40/90/0.18	40/90/0.18
8	1032/2705/1.58	1020/2668/1.42	997/2279/1.28	8780/10109/1.57
9	2388/4881/2.40	2503/5048/3.06	4658/7644/2.48	14945/16013/9.92
10	477/871/2.66	478/858/2.62	20010/98744/4.70	20010/292528/9.39
11	182/423/1.03	174/418/1.09	14053/39805/1.28	15593/489487/8.58
12	113/302/0.16	113/302/0.20	428/6427/2.19	609/11752/4.81
13	80/226/0.11	78/222/0.08	113/234/0.08	291/509/0.26
14	61/131/0.50	61/131/0.56	906/23792/1.66	318/6032/3.76
15	460/991/0.62	452/969/0.59	636/1006/0.73	964/1479/1.25
16	66/132/0.03	66/132/0.04	60/120/0.03	1043/1116/0.38
17	70/160/0.11	70/160/0.06	207/339/0.19	110/230/0.10
18	753/1577/0.79	791/1668/0.85	821/1545/0.78	3732/4630/3.99
19	74/158/0.33	74/158/0.42	108/1352/2.44	303/7194/2.66
20	110/349/0.41	109/349/0.37	135/321/0.42	154/339/0.45
21	806/3224/1.60	600/1665/1.26	875/14122/5.89	929/10442/9.02
22	72/275/0.51	72/285/0.49	2104/2442/3.61	161/440/0.92
23	4470/9572/1.33	5033/10748/2.42	18912/38658/8.87	20010/25808/6.95
24	62/201/0.42	62/201/0.40	1853/6983/3.39	2527/76854/9.01
25	459/1091/0.60	521/1192/0.78	304/606/0.40	1199/1793/1.55
26	56/153/0.08	65/373/0.13	128/1103/0.37	2697/14700/7.09
27	85/203/0.11	85/203/0.12	91/193/0.13	132/264/0.16
28	534/1139/0.65	514/1073/0.68	288/558/0.35	556/925/0.60
29	540/1274/0.62	537/1267/0.58	852/1783/0.98	1014/2180/1.14
30	576/1440/0.96	591/1504/1.05	20010/98171/6.44	20010/317766/8.02
31	113/236/0.16	113/236/0.11	79/168/0.10	147/287/0.13
32	813/2181/3.28	735/1997/3.03	20010/91480/9.47	20010/179051/5.16
33	98/268/0.18	98/268/0.17	631/11069/5.15	837/17999/8.99
34	346/766/0.48	348/766/0.50	716/1148/0.90	744/1213/0.93
35	7635/12820/8.59	7554/12715/8.73	8375/13146/9.98	8539/12513/15.46
36	280/978/0.43	280/978/0.35	330/695/0.37	401/868/0.47
37	217/534/0.31	217/534/0.27	610/6778/2.40	820/11112/5.50
38	121/287/0.14	120/285/0.13	1565/42467/4.89	1624/45918/6.43
39	150/329/0.64	153/328/0.65	174/290/0.54	193/323/0.69
40	107/217/0.65	107/217/0.68	253/426/1.03	4281/4461/11.17
41	120/330/0.23	120/330/0.25	118/286/0.19	124/298/0.20
42	3832/9998/2.51	3373/8928/7.18	3685/8619/8.30	17419/22467/5.83
43	40/80/0.11	40/80/0.08	99/119/0.19	99/119/0.19
44	50/110/0.10	50/110/0.05	50/110/0.02	70/282/0.13
45	43/184/0.08	43/184/0.11	12047/91618/9.93	15601/521624/4.14
46	427/1323/2.56	427/1320/2.60	409/1040/2.07	597/1232/2.51
47	64/249/0.09	64/249/0.06	133/380/0.15	143/393/0.40
48	308/798/1.39	293/772/1.28	2549/27198/2.61	15662/156182/6.10
49	22/89/0.11	22/89/0.13	1377/37674/8.58	1571/43940/8.14
50	20/50/0.03	20/50/0.02	20/50/0.02	20/50/0.03
51	92/1755/2.25	42/136/0.17	1620/5439/3.43	1680/46332/4.04
52	107/418/0.16	107/418/0.15	125/360/0.14	125/360/0.16
53	6199/52426/6.75	6199/52426/6.78	4160/9534/3.23	2233/8070/9.66
54	51/151/0.20	51/151/0.19	75/173/0.25	77/144/0.20
55	60/140/0.19	60/140/0.19	60/120/0.14	60/120/0.17
56	70/140/0.20	70/140/0.17	70/140/0.24	80/160/0.22
57	79/158/0.22	79/158/0.22	79/158/0.24	86/172/0.23
58	143/570/0.25	143/570/0.25	177/506/0.25	177/506/0.25
59	188/498/0.29	172/453/0.27	209/460/0.30	641/917/1.01
60	83/236/0.13	83/236/0.11	1615/43549/5.17	2005/57225/7.75
Total	37602/124896/60.1	37426/121943/70.14	167737/10741186/139.61	271227/7136001/214.33