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Table 3 The numerical results of Algorithm 3.1 for some test problems (\(\varepsilon =10^{-4}\))

From: A simple approximated solution method for solving fractional trust region subproblems of nonlinearly equality constrained optimization

Pro

n

Starting point

Algorithm

Iter

nf/ng

Qg

CPU (s)

1

50

(2,1.5,0.5,…,2,1.5,0.5,2,1.5)

CTR

66

66/59

7.675845(−5)

0.300518

FTR

29

29/23

5.866993(−5)

0.627469

101

(2,1.5,0.5,…,2,1.5,0.5,2,1.5)

CTR

137

137/128

9.543858(−5)

1.619127

FTR

37

37/29

2.970168(−5)

1.184047

200

(2,1.5,0.5,…,2,1.5,0.5,2,1.5)

CTR

∗

∗/∗

∗

∗

FTR

33

33/27

7.135361(−5)

1.942937

5

25

(35,11,5,−5,…,35,11,5,−5,35,11,5)

CTR

76

76/64

7.377510(−5)

0.232441

FTR

58

58/55

8.181980(−5)

0.546569

61

(35,11,5,−5,…,35,11,5,−5,35,11,5)

CTR

∗

∗/∗

∗

∗

FTR

74

74/64

7.910359(−5)

1.934600

10

30

(−1,1,…,−1,1)

CTR

81

81/75

5.527921(−5)

0.202645

FTR

26

26/21

3.795910(−6)

0.355148

100

(−1,1,…,−1,1)

CTR

26

26/21

1.689243(−5)

0.197726

FTR

21

21/16

1.357598(−5)

0.657030

200

(−1,1,…,−1,1)

CTR

45

45/36

7.697442(−6)

0.713368

FTR

28

28/20

1.204414(−5)

1.409634

400

(−1,1,…,−1,1)

CTR

80

80/70

1.815889(−5)

5.648017

FTR

24

24/18

9.612549(−5)

3.302268