Table 1 Comparison between adaptive trust region methods and a new method.
From: A new nonmonotone adaptive trust region line search method for unconstrained optimization
Problem | n | \(n_{f}\)/\(n_{i}\) | |||||
|---|---|---|---|---|---|---|---|
SNTR \(\Delta_{0} = 0.1\) | SNTR \(\Delta_{0} = 10\) | SNTR \(\Delta_{0} = 100\) | ATRG | ATRN | NLS | ||
Ext. Rose | 4 | 690/353 | 475/243 | 364/185 | 168/88 | 94/65 | 70/57 |
Ext. Beale | 4 | 504/254 | 27/14 | 29/15 | 41/21 | 27/14 | 19/18 |
Penalty i | 2 | 129/67 | 38/21 | 34/19 | 33/18 | 47/26 | 29/19 |
Pert. Quad | 6 | 151/80 | 33/17 | 31/16 | 41/21 | 31/16 | 29/1 |
Raydan 1 | 10 | 1445/762 | 40/21 | 40/21 | 40/21 | 40/21 | 22/15 |
Raydan 2 | 4 | 251/128 | 14/8 | 14/8 | 13/8 | 13/8 | 11/6 |
Diagonal 1 | 4 | 112/58 | 21/11 | 21/11 | 21/11 | 21/11 | 13/12 |
Diagonal 2 | 2 | 289/147 | 18/10 | 18/10 | 16/9 | 16/9 | 19/10 |
Diagonal 3 | 10 | 128/66 | 33/17 | 33/17 | 43/22 | 33/17 | 28/15 |
Hager | 10 | 134/69 | 29/15 | 29/15 | 27/14 | 27/14 | 31/16 |
Gen. Trid 1 | 20 | 1234/618 | 49/25 | 45/23 | 50/26 | 51/26 | 37/23 |
Ext. Trid 1 | 20 | 65/35 | 16/9 | 33/17 | 16/9 | 16/9 | 24/16 |
Ext. TET | 50 | 195/103 | 17/9 | 17/9 | 16/9 | 17/9 | 17/9 |
Diadonal 4 | 50 | 798/429 | 29/15 | 19/10 | 7/4 | 7/4 | 6/5 |
Ext. Him | 50 | 134/69 | 20/11 | 25/13 | 58/44 | 28/15 | 18/10 |
Gen. White | 50 | 666/363 | 271/151 | 719/384 | 382/200 | 312/186 | 243/142 |
Ext. Powell | 4 | 892/455 | 654/329 | – | 264/133 | 237/125 | 157/98 |
Full. He. FH3 | 10 | 106/55 | 13/7 | 11/6 | 13/7 | 13/7 | 8/7 |
Ext. BD1 | 100 | 278/143 | 33/19 | 31/17 | 41/23 | 268/151 | 26/19 |
Pert. Quad | 200 | 290/165 | 141/72 | 104/53 | 188/96 | 99/51 | 41/38 |
Ext. Hie | 16 | 1821/1000 | – | – | 240/143 | 198/137 | 119/60 |
Quad. QF1 | 4 | 683/377 | 17/9 | 17/9 | 17/9 | 15/8 | 11/10 |
FLET34 | 50 | 24/13 | 167/101 | 225/127 | 183/110 | 168/98 | 210/108 |
ARWHEAD | 200 | 172/91 | 44/25 | 56/30 | 55/42 | 21/14 | 24/13 |
NONDIA | 200 | 75/38 | 102/52 | 71/36 | 116/61 | 63/32 | 63/32 |
DQDRTIC | 200 | 363/191 | 50/27 | 54/29 | 43/23 | 36/25 | 27/23 |
EG2 | 10 | 458/234 | 25/14 | 25/14 | 24/14 | 24/14 | 14/14 |
Bro. Trid. | 200 | 2797/1504 | 1609/827 | 356/187 | 404/216 | 268/176 | 258/133 |
A. Per. Quad | 16 | 253/133 | 43/22 | 45/23 | 61/34 | 41/31 | 43/32 |
Pert. Trid | 20 | 252/135 | 59/30 | 57/29 | 79/47 | 57/42 | 56/43 |
LIARWHD | 50 | 114/60 | – | 295,148 | 257/176 | 255/167 | 249/132 |
Ext. DENSCH | 100 | 71/37 | 34/18 | 51/26 | 239/154 | 50/26 | 239/154 |
HIMMELH | 4 | 58/31 | 91/61 | 90/56 | 19/18 | 75/41 | 17/16 |
ENGVAL1 | 10 | 165/90 | 71/38 | 71/37 | 65/35 | 63/34 | 50/36 |
EDENSCH | 100 | 1265/633 | 27/15 | 3073/1583 | 21/12 | 23/13 | 35/18 |