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 |