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Table 1 The results for the methods on the tested problems

From: Three modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property

P n TMPRP1 CG_DESCENT DTPRP
Freudenstein and Roth 100 52/1,017/0.4,688 53/1,030/0.4219 94/2,037/0.8125
Trigonometric 5,000 118/539/5.6094 75/603/5.6250 57/170/2.2813
Extended Rosenbrock 5,000 44/868/1.7344 119/2,195/3.6875 54/956/1.8281
Generalized Rosenbrock 10 223/5,114/1.2500 567/13,632/3.5156 305/6,522/1.6719
White 1,000 48/874/1.3594 101/2,321/3.3438 71/1,474/2.0625
Beale 5,000 45/933/3.7344 98/2,182/8.3906 43/555/2.2031
Penalty 5,000 30/593/1.2969 26/516/1.1094 F
Perturbed quadratic 100 92/1,674/0.5469 114/1,974/0.6563 99/2,302/0.6875
Raydan 1 500 171/3,083/1.9219 231/3,882/2.3125 150/2,333/1.4688
Raydan 2 5,000 5/6/0.3750 6/60/0.6250 6/7/0.3438
Diagonal 1 100 88/1,462/0.6250 74/880/0.4063 83/1,608/0.6563
Diagonal 2 100 780/781/0.5938 104/341/0.1875 780/781/0.5313
Diagonal 3 100 101/1,492/0.7188 154/2,321/1.0781 77/767/0.4219
Hager 100 44/640/0.3281 32/251/0.1563 34/403/0.2188
Generalized tridiagonal 1 1,000 41/578/1.4844 31/403/1.0469 58/1,078/2.8594
Extended tridiagonal 1 1,000 41/432/1.1250 40/497/1.2188 46/724/1.8281
Extended three expo terms 5,000 45/759/5.5156 31/246/2.0781 21/174/1.5469
Generalized tridiagonal 2 1,000 56/785/1.3594 404/11,638/19.5938 61/1031/1.7813
Diagonal 4 5,000 48/815/1.3906 128/2,383/3.6406 55/673/1.1719
Diagonal 5 5,000 4/5/0.2969 4/8/0.3906 4/5/0.3281
Extended Himmelblau 5,000 30/438/1.0625 23/214/0.7500 20/178/0.7344
Generalized PSC1 5,000 222/1,100/5.7344 672/5,554/27.0156 F
Extended PSC1 5,000 55/916/5.0156 24/173/1.5156 24/187/1.4375
Extended Powell 5,000 193/2,649/17.4844 F 536/7,005/42.2031
Extended BD1 5,000 35/431/1.5156 49/856/2.8281 33/452/1.6250
Extended Maratos 1,000 66/1,121/0.6563 F 136/2,206/1.2344
Extended Cliff 5,000 48/262/1.6094 123/1,275/6.5000 F
Quadratic diagonal perturbed 5,000 433/6,793/3.6875 F 247/3,834/2.1094
Extended Wood 5,000 199/2,976/5.7188 F 131/2,075/4.1094
Extended Hiebert 5,000 2/32/0.4844 2/33/0.5313 3/62/0.5469
Quadratic QF1 5,000 731/12,453/19.8438 790/13,180/20.1875 882/14,508/22.3906
Extended QP1 1,000 65/1,662/1.0156 25/361/0.2813 16/157/0.1875
Extended QP2 5,000 64/988/5.1719 143/2,919/13.9219 78/1,170/6.4063
Quadratic QF2 5,000 777/14,146/24.6406 968/17,331/31.9219 814/14,358/24.7344
Extended EP1 5,000 101/2,391/6.6094 12/195/1.0000 136/3,136/8.0781
Extended tridiagonal 2 5,000 46/615/2.0156 63/1,270/3.4844 32/170/0.9219
BDQRTIC 100 159/2,473/0.8438 F 185/3,133/1.0156
TRIDIA 100 310/4,816/1.5938 440/7,143/2.2344 364/6,190/1.8281
ARWHEAD 5,000 35/702/2.2813 F F
NONDIA 5,000 30/626/1.8906 F 209/4,327/10.7344
NONDQUAR 5 713/779/0.4531 97/809/0.2813 F
DQDRTIC 5,000 80/1,234/2.7031 117/2,386/4.8750 81/1,108/2.4688
EG2 100 165/2,715/1.5,000 85/1,136/0.7969 F
DIXMAANA 5,001 21/191/7.0938 13/177/6.4688 10/70/2.8281
DIXMAANB 5,001 22/45/2.0000 13/127/4.7344 7/14/0.8750
DIXMAANC 5,001 17/136/5.1719 15/231/8.7500 6/17/0.9219
DIXMAANE 102 346/451/0.7031 186/5,359/5.4844 321/325/0.5313
Partial perturbed quadratic 100 87/1,905/1.6094 116/2,180/1.6719 77/1,326/0.9844
Broyden tridiagonal 5,000 114/1,927/5.1719 101/1,884/4.9531 119/2,029/5.2656
Almost perturbed quadratic 5,000 854/19,329/30.2969 F 866/19,516/32.0938
Tridiagonal perturbed quadratic 5,000 760/16,744/42.7813 959/22,230/52.9063 774/17,831/43.9063
EDENSCH 1,000 40/615/1.7188 35/450/1.1875 49/1,273/3.0938
HIMMELBHA 5,000 15/69/1.4063 F 17/18/0.6406
STAIRCASE S1 100 341/5,058/1.5781 F 510/7,591/2.4844
LIARWHD 5,000 39/727/1.9688 165/3,873/9.7500 262/6,799/16.2500
DIAGONAL 6 5,000 5/6/0.3594 6/60/0.5313 6/7/0.3594
DIXON3DQ 100 578/9,208/3.0625 F 499/7,241/2.1563
ENGVAL1 5,000 36/611/1.7344 52/1,264/3.3906 F
DENSCHNA 5,000 23/249/1.9063 27/318/2.5938 19/93/1.0469
DENSCHNB 5,000 21/54/0.4844 10/79/0.4531 20/327/0.9063
DENSCHNC 5,000 23/191/2.6094 34/357/4.5938 F
DENSCHNF 5,000 25/343/1.1094 24/348/1.1250 23/363/1.2656
SINQUAD 100 505/10,201/4.1250 F F
BIGGSB1 100 489/5,248/1.7031 F 533/5,660/1.6406
Extended block-diagonal 1,000 30/506/0.8906 36/508/0.8750 26/374/0.5938
Generalized quartic 1 5,000 21/159/0.7500 18/342/1.0469 36/777/1.8594
DIAGONAL 7 5,000 53/2,509/14.1563 54/2,477/13.8125 F
DIAGONAL 8 5,000 57/2,710/18.3906 56/2,622/17.5781 F
Full Hessian 5,000 17/239/1.6094 18/305/1.9688 46/1,643/8.8750
SINCOS 5,000 26/250/1.5313 22/132/1.1719 F
Generalized quartic 2 5,000 48/996/2.4688 35/606/1.4375 39/704/1.6250
EXTROSNB 5,000 39/741/1.7500 159/7,756/14.8750 43/1,010/2.3281
ARGLINB 100 101/5,024/1.7969 111/5,498/1.7813 23/691/0.3125
FLETCHCR 5,000 61/1,662/4.0469 36/661/1.7813 61/1,976/4.7969
HIMMELBG 2 F 2/4/0.0313 F
HIMMELBH 5,000 18/103/0.7969 23/224/1.1406 16/91/0.6719
DIAGONAL 9 5,000 1/3/0.3594 1/3/0.3906 1/3/0.3594