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Journal of Inequalities and Applications

Table 1 A list of test problem functions

From: An efficient modification of the Hestenes-Stiefel nonlinear conjugate gradient method with restart property

No.

Function

Dimension/s

Initial points

1

Extended White & Holst function

2, 500, 1,000, 5,000, 10,000

(−1.2,1,−1.2,1,…,−1.2,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

2

Extended Rosenbrock function

2, 500, 1,000, 5,000, 10,000

(−1.2,1,−1.2,1,…,−1.2,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

3

Six hump function

2

(1,1), (5,5), (10,10), (15,15)

4

Extended Beale function

2, 500, 1,000, 5,000, 10,000

(−1,−1,…,−1), (0.5,0.5,…,0.5), (10,10,…,10), (1,1,…,1)

5

Three hump function

2

(1,1), (5,5), (10,10), (15,15)

6

Extended Himmelblau function

2, 500, 1,000, 5,000, 10,000

(1,1,…,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

7

Diagonal 2 function

2, 500, 1,000, 5,000, 10,000

(0.2,0.2,…,0.2), (0.25,0.25,…,0.25), (0.5,0.5,…,0.5), (1,1,…,1)

8

NONSCOMP function

2, 500, 1,000, 5,000, 10,000

(1,1,…,1), (−1,−1,…,−1), (−2,−2,…,−2), (−5,−5,…,−5)

9

Extended DENSCHNB function

2, 500, 1,000, 5,000, 10,000

(1,1,…,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

10

Shallow function

2, 500, 1,000, 5,000, 10,000

(−2,−2,…,−2), (2,2,…,2), (5,5…,5), (10,10,…,10)

11

Booth function

2

(1,1), (5,5), (10,10), (15,15)

12

Extended quadratic penalty function QP2

2, 500, 1,000, 5,000, 10,000

(2,2,…,2), (5,5,…,5), (10,10,…,10), (15,15,…,15)

13

DIXMAANA function

300, 6,000, 9,000, 12,000

(1,1,…,1), (2,2,…,2), (3,3,…,3), (5,5,…,5),

14

DIXMAANB function

300, 6,000, 9,000, 12,000

(1,1,…,1), (2,2,…,2), (3,3,…,3), (5,5,…,5),

15

NONDIA function

2, 500, 1,000, 5,000, 10,000

(−2,−2,…,−2), (−1,−1,…,−1), (0,0,…,0), (1,1,…,1)

16

Extended tridiagonal 1 function

2, 500, 1,000, 5,000, 10,000

(1,1,…,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

17

DQDRTIC function

2, 500, 1,000, 5,000, 10,000

(−1,−1,…,−1), (1,1,…,1), (2,2,…,2), (3,3,…,3)

18

Diagonal 4 function

2, 500, 1,000, 5,000, 10,000

(1,1,…,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

19

Extended Cliff function

2, 500, 1,000, 5,000, 10,000

(1,1,…,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

20

Shallow function

2, 500, 1,000, 5,000, 10,000

(−2,−2,…,−2), (2,2,…,2), (5,5,…,5), (10,10,…,10)

21

NONDIA (Shanno-78)

2, 500, 1,000, 5,000, 10,000

(−2,−2,…,−2), (−1,−1,…,−1), (0,0,…,0), (1,1,…,1)

22

Raydan 2 Function

2, 500, 1,000, 5,000, 10,000

(1,1,…,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

23

Extended block diagonal BD1 function

2, 500, 1,000, 5,000, 10,000

(0.1,0.1,…,0.1), (0.2,0.2,…,0.2), (0.3,0.3,…,0.3), (0.4,0.4,…,0.4)

24

Generalized tridiagonal 1 function

2, 500, 1,000, 5,000, 10,000

(1,1,…,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

25

Diagonal 4 function

2, 500, 1,000, 5,000, 10,000

(1,1,…,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

26

Extended Powell function

2, 500, 1,000, 5,000, 10,000

(1,1,…,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

27

Perturbed quadratic function

2, 500, 1,000, 5,000, 10,000

(0.5,0.5,…,0.5), (2,2,…,2), (1,1,…,1), (10,10,…,10)

28

A quadratic function QF2

2, 500, 1,000, 5,000, 10,000

(0.5,0.5,…,0.5), (1,1,…,1), (5,5,…,5), (10,10,…,10)

29

Sum squares function

2, 500, 1,000, 5,000, 10,000

(−5,−5,…,−5), (−1,−1,…,−1), (1,1,…,1), (5,5,…,5)

30

Zettl function

2

(1,1,…,1), (5,5,…,5), (10,10,…,10), (15,15,…,15)

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