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

Table 1

Comparisons of new algorithm against (LS) & (CD) 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	LS; NOI/NOFG/TIME	CD; NOI/NOFG/TIME
1	99/252/0.14	101/263/0.14	323/7045/2.31	414/9608/2.64
2	408/884/2.02	405/880/1.97	412/888/1.98	395/878/2.08
3	853/2183/1.06	830/2171/0.98	823/2159/1.02	824/2154/0.97
4	123/308/0.14	123/308/0.15	114/300/0.17	121/314/0.15
5	100/388/0.15	100/388/0.20	274/5586/1.14	167/1918/0.77
6	585/995/1.56	585/995/1.54	6576/19689/4.54	6848/20496/5.70
7	30/80/0.15	30/80/0.13	40/100/0.21	40/100/0.16
8	1032/2705/1.58	1020/2668/1.42	1033/2768/1.49	1026/2972/1.52
9	2388/4881/2.40	2503/5048/3.06	3520/7182/7.49	3676/7485/8.83
10	477/871/2.66	478/858/2.62	18795/503441/7.60	19346/518146/9.14
11	182/423/1.03	174/418/1.09	8669/270951/5.83	8252/257171/6.83
12	113/302/0.16	113/302/0.20	318/3881/1.69	279/2792/5.80
13	80/226/0.11	78/222/0.08	73/241/0.10	73/241/0.09
14	61/131/0.50	61/131/0.56	124/2140/7.12	160/2833/3.54
15	460/991/0.62	452/969/0.59	456/953/0.61	467/997/0.64
16	66/132/0.03	66/132/0.04	67/134/0.14	68/136/0.06
17	70/160/0.11	70/160/0.06	69/158/0.10	71/162/0.08
18	753/1577/0.79	791/1668/0.85	691/1477/0.74	782/1687/0.82
19	74/158/0.33	74/158/0.42	123/1905/2.31	70/150/0.30
20	110/349/0.41	109/349/0.37	114/334/0.43	111/329/0.41
21	806/3224/1.60	600/1665/1.26	429/1895/4.93	561/5284/5.69
22	72/275/0.51	72/285/0.49	84/366/0.70	2084/2322/9.54
23	4470/9572/1.33	5033/10748/2.42	20010/168275/4.95	19334/128670/5.02
24	62/201/0.42	62/201/0.40	546/15413/3.73	495/13595/3.48
25	459/1091/0.60	521/1192/0.78	494/1101/0.65	531/1154/0.76
26	56/153/0.08	65/373/0.13	56/155/0.06	66/328/0.12
27	85/203/0.11	85/203/0.12	80/190/0.07	80/190/0.09
28	534/1139/0.65	514/1073/0.68	493/1055/0.63	492/1075/0.61
29	540/1274/0.62	537/1267/0.58	941/2237/1.03	943/2239/1.11
30	576/1440/0.96	591/1504/1.05	19026/581537/2.57	18144/543276/2.03
31	113/236/0.16	113/236/0.11	118/245/0.11	123/253/0.11
32	813/2181/3.28	735/1997/3.03	18140/560188/8.67	18320/564064/8.04
33	98/268/0.18	98/268/0.17	359/5355/2.21	387/6200/3.06
34	346/766/0.48	348/766/0.50	356/786/0.44	332/732/0.44
35	7635/12820/8.59	7554/12715/8.73	7463/12576/8.29	7183/12051/8.37
36	280/978/0.43	280/978/0.35	264/935/0.45	273/978/0.39
37	217/534/0.31	217/534/0.27	221/551/0.31	219/546/0.31
38	121/287/0.14	120/285/0.13	814/20969/8.83	786/20117/7.46
39	150/329/0.64	153/328/0.65	141/305/0.59	137/297/0.58
40	107/217/0.65	107/217/0.68	144/1165/3.67	124/476/1.35
41	120/330/0.23	120/330/0.25	100/290/0.17	100/290/0.18
42	3832/9998/2.51	3373/8928/7.18	3404/9046/8.47	3182/8618/7.82
43	40/80/0.11	40/80/0.08	40/80/0.12	40/80/0.12
44	50/110/0.10	50/110/0.05	50/110/0.09	50/110/0.05
45	43/184/0.08	43/184/0.11	3903/129109/7.10	7265/242193/4.78
46	427/1323/2.56	427/1320/2.60	413/1307/2.53	428/1252/2.44
47	64/249/0.09	64/249/0.06	118/447/0.22	114/425/0.19
48	308/798/1.39	293/772/1.28	773/7349/0.72	1731/23050/5.88
49	22/89/0.11	22/89/0.13	316/8561/9.47	298/8022/8.33
50	20/50/0.03	20/50/0.02	20/50/0.00	20/50/0.04
51	92/1755/2.25	42/136/0.17	361/9646/9.02	315/8202/8.61
52	107/418/0.16	107/418/0.15	107/418/0.16	107/418/0.16
53	6199/52426/6.75	6199/52426/6.78	8071/53291/6.20	8071/53291/9.30
54	51/151/0.20	51/151/0.19	51/151/0.21	51/151/0.18
55	60/140/0.19	60/140/0.19	60/140/0.18	60/140/0.20
56	70/140/0.20	70/140/0.17	70/140/0.19	70/140/0.16
57	79/158/0.22	79/158/0.22	79/158/0.24	74/148/0.22
58	143/570/0.25	143/570/0.25	143/570/0.23	143/570/0.21
59	188/498/0.29	172/453/0.27	176/449/0.27	177/461/0.22
60	83/236/0.13	83/236/0.11	985/27409/9.27	917/25010/8.38
Total	37602/124886/55.54	37426/121643/59.2	131933/2455353/154.98	136949/1242169/166.56