Journal of Mathematics

Research Article

A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence

Table 1

A list of test problem functions.
ProblemBZAU
NI/GE/FE/CT		TMPRP1
NI/GE/FE/CT
Extended white and holst function31/223/191/1.464732/193/160/1.1246
31/223/191/1.84532/193/160/1.4398
Extended Rosenbrock function28/170/141/1.157321/110/88/0.8869
28/170/141/1.15221/110/88/0.9232
Extended Himmelblau function7/34/26/0.644610/47/36/0.6638
7/34/26/0.754411/51/39/0.697
7/34/26/0.916312/55/42/1.0252
Extended DENSCHNB function5/22/16/0.61356/26/19/0.5955
6/26/16/0.686/26/19/0.7011
Shallow function9/41/31/0.61888/39/30/0.6341
9/41/31/0.72918/39/30/0.764
DIXMAANA function8/35/26/1.6510/43/32/1.7494
8/35/26/2.133910/67/56/2.7067
NONDIA8/59/50/0.697611/66/54/0.7215
14/84/69/1.495816/90/73/1.5903
DQDRTIC5/21/15/0.62025/21/15/0.658
5/21/15/0.59975/21/15/0.6591
Extended Block Diagonal BD 132/37000/28750/1.982235/73750/64750/2.6201
32/75500/59000/2.455736/147000/128500/4.261
Extended Tridiagonal 14/18/13/0.57891694/5096/3401/18.6813
2072/7767/5694/130.172F
Diagonal 42/9/6/0.57812/9/6/0.589
2/9/6/0.61382/9/6/0.623
Extended Powell400/41100/31075/7.634692/9925/7600/2.4096
400/205500/155375/7.5892/49625/38000/2.3136
Diagonal 244/135/90/1.00848/147/98/1.2072
964/2895/1930/12.4522968/2907/1938/12.5155
Sum Squares57/229/171/1.484657/229/171/1.5077
165/661/495/3.1385165/661/495/3.2041
SINQUAD75/376/300/2.0587138/653/514/3.5782
131/630/498/3.9387594/2252/1657/11.1859
DIXMAANC6/29/22/0.74587/33/25/0.7998
6/29/22/0.76677/33/25/0.7857
DIXMAANE60/300/239/2.1251434/1374/939/7.1568
244/1220/975/25.8693F
DIXMAANG66/330/263/2.3892681/2073/1391/9.6909
2961/13363/10401/281.4836F
DIXMAANI20/90/69/0.896543/136/92/1.0161
287/1269/961/6.297342/1375/1032/6.5883
DIXMAANK21/94/72/0.8752/163/110/0.99
684/2069/1384/9.0948695/2904/1398/9.2842
DENSCHNA8/40/31/0.64628/37/28/0.7929
8/40/31/0.82368/37/28/0.8122
DENSCHNB5/22/16/0.6746/26/19/0.997
5/22/16/0.65596/26/19/0.6583
DENSCHNC7/38/30/0.75998/42/33/0.6927
7/38/30/0.83278/42/33/0.8875
ARGLINB2/9/6/0.57142/9/6/0.5631
2/9/6/0.57772/9/6/0.6239
Power2/9/6/0.55872/9/6/0.5702
66/265/198/1.767266/265/198/1.7369
Fletcher22/120/97/0.96426/143/116/1.0727
242/1333/1090/8.6331278/1495/1216/9.7661
HIMMELBH9/77/67/0.83988/74/65/1.1388
9/77/67/1.13248/74/65/1.7183
NONDQUAR660/2649/1988/14.3065739/2964/2224/16.1369
7170/28703/21532/110.70F
Generalized quartic GQ111/47/35/0.70613/55/41/0.6912
11/47/35/0.98712/52/39/1.219
Generalized quartic GQ224/106/81/0.949726/115/88/1.0062
23/102/78/0.941224/107/82/0.9761
Extended Quadratic Penalty12/61/48/0.706710/43/32/0.642
15/92/76/1.23518/119/100/1.2217
ARWHEAD8/36/27/0.62497/32/24/0.5877
7/39/31/0.61066/35/28/0.6174
Quartic3941/11826/7884/56.8883945/11838/7892/59.0699
5358/16077/10718/80.0295362/16089/10726/78.05
Extrosnb0/1/0/0.50270/1/0/0.5208
0/496/334/0.51880/1/0/0.5168
LIARWHD11/56/44/0.735412/66/53/0.794
16/94/77/0.886120/134/113/1.3092
ENGVAL87/36/26/0.65828/37/28/0.6912
FF
Hager4/17/12/0.61034/17/12/0.5686
25/151/125/1.208625/102/76/0.9215
Extended Wood91/509/417/3.0717116/627/510/3.6229
68/423/354/2.767887/535/447/3.3762
BIGGSB11579/6316/4736/31.32711627/6508/4880/32.1275
2463/9852/7388/48.43663509/14036/10526/68.93
Extended Beale15/71/55/0.754112/59/46/0.7065
15/71/55/0.814312/59/46/0.8638
Extended Penalty9/43/33/0.634110/46/35/0.6735
37/252/214/1.7596F
Extended Maratos Function33/223/189/2.123431/213/181/1.5054
F31/213/181/1.5017
Quadratic QF2 Function6/26/19/0.61226/26/19/0.6209
293/1269/975/6.6934277/996/768/5.1248
SINCOS8/39/30/0.862312/51/38/0.9807
8/39/30/1.128912/51/38/1.2905
STAIRCASE S131/125/93/1.055532/129/96/1.0384
135/540/404/2.7473197/790/592/4.0499
GENROSEN-225/159/133/1.337921/110/88/0.9879
6889/36000/29110/185.574/488/413/3.4692
TRIDIAGONAL DOUBLE BORDED395/1585/1189/7.8008540/2165/1624/11.11
773/3099/2325/15.4811016/4073/3056/20.09
EDENSCH FUNCTION3090/9276/6185/40.92973094/9288/6193/34.4141
3090/9276/6185/135.2323094/9288/6193/131.676
DENSCHNF10/59/48/0.920512/73/60/0.9032
10/59/48/0.754612/73/60/0.8977
Generalized Triagonal-123/95/71/0.9284F
25/124/98/1.582224/100/75/0.9883
Generalized Triagonal-243/205/161/1.22535/165/129/1.5369
39/188/148/1.254839/191/151/1.2668
Extended Trigonomenctric313/965/651/5.1384324/990/665/5.2108
97/437/339/2.6942318/997/678/5.3339
DIAGONAL-15/22/16/0.64676/27/20/0.6174
23/95/71/0.88925/103/77/0.9587
EG332/138/105/1.171233/141/107/1.1336
35/180/144/1.4381F
Extended Three Exponential8/1700/1250/0.64416/1300/950/0.6111
8/17000/12500/0.9996/13000/9500/0.8019
Extended Freudenstein and Roth16/91/74/0.7806F
16/141/124/1.0795F
Dixon3DQ3049/12196/9146/49.193409/13636/10226/55.20
4959/19836/14876/80.416473/25892/19418/117.9
Quadratic Qf1187/749/561/4.2752187/749/561/4.3368
426/1705/1278/10.7051426/1705/1278/11.6042
Extended Quadratic penalty Q246/466/419/2.975551/576/524/4.0679
61/740/678/6.62786/1052/970/9.3083
Sphere1/5/3/0.55811/5/3/0.549
1/5/3/0.54981/5/3/0.5447
Raydan1101/304/202/1.6957105/316/210/2.0696
66/266/199/1.527669/278/208/2.0739
BDQRTIC37/179/141/1.165352/240/187/1.4611
FF
DIXMAANJ23/88/64/0.80952/162/109/1.0504
3015/13079/10063/63.4987074/21256/14181/93.00
DIXMAANB5/23/17/0.58486/27/20/0.652
8/34/25/0.9458/34/25/0.954
DIXMAAND8/38/29/0.9329/42/32/0.9416
7/34/26/1.064110/46/35/1.215
DIXMAANF90/451/360/3.3861327/3998/2670/19.805
1071/4832/3760/29.36613488/10489/7000/103.27
DIXMAANH81/408/326/2.63331319/3974/2654/17.820
1476/6413/4936/76.603462/10409/6946/121.09
DIXMAANL16/76/59/0.772652/164/111/1.1245
3023/13115/10091/57.847031/21130/14098/85.66
Raydan 24/17/12/0.59852/9/6/0.5584
5/21/15/0.63522/9/6/0.5593
Perturbed Quadratic187/749/561/3.9731187/749/561/3.7987
425/1701/1275/11.039425/1701/1275/10.9626
A Quadratic Function6/26/19/0.63346/26/19/0.6101
91/396/304/2.225296/417/320/2.421
TRIDIA240/961/720/5.146240/961/720/5.5388
349/1397/1047/7.1665349/1397/1047/7.090
Zett112/52/39/0.657814/61/46/0.6748
Six hump7/31/23/0.64828/36/27/0.6714
Booth2/9/6/0.57222/9/6/0.5513
Three hump6/28/21/0.59597/31/23/0.6031
EG24/20/15/0.60115/26/20/1.3894