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Journal of Inequalities and Applications

Table 1 Numerical results

From: A modified nonmonotone BFGS algorithm for unconstrained optimization

Problem

Dim

BFGS-WP NI/NFG/Time

BFGS-WP-Zhang NI/NFG/Time

BFGS-Non NI/NFG/Time

BFGS-M-Non NI/NFG/Time

ROSE

2

35/590/4.506480e−002

31/611/4.882020e−002

2/19/6.259000e−003

2/19/6.259000e−003

FROTH

2

9/116/1.376980e−002

7/90/1.001440e−002

2/19/6.259000e−003

2/19/7.510800e−003

BADSCP

2

43/706/5.507920e−002

43/706/5.507920e−002

8/264/2.753960e−002

8/264/2.753960e−002

BADSCB

2

3/60/1.126620e−002

3/60/1.001440e−002

3/32/7.510800e−003

3/32/6.259000e−003

BEALE

2

15/220/2.128060e−002

16/226/2.002880e−002

2/19/6.259000e−003

2/19/6.259000e−003

JENSAM

2

2/42/1.126620e−002

2/42/1.001440e−002

2/19/6.259000e−003

2/19/8.762600e−003

HELIX

3

34/483/4.381300e−002

23/325/3.004320e−002

169/2,191/2.090506e−001

87/1,163/1.114102e−001

BARD

3

16/229/3.004320e−002

14/182/2.503600e−002

72/930/1.226764e−001

72/930/1.226764e−001

GAUSS

3

2/19/6.259000e−003

2/19/6.259000e−003

2/19/7.510800e−003

2/19/7.510800e−003

MEYER

3

2/42/1.376980e−002

2/42/1.251800e−002

2/32/1.126620e−002

2/32/1.251800e−002

GULF

3

2/42/1.502160e−002

2/42/1.502160e−002

2/19/3.755400e−003

2/19/1.001440e−002

BOX

3

2/42/1.251800e−002

2/42/1.126620e−002

2/19/7.510800e−003

2/19/8.762600e−003

SING

4

20/280/2.503600e−002

18/269/2.503600e−002

2/19/6.259000e−003

2/19/7.510800e−003

WOOD

4

19/271/2.628780e−002

20/289/2.753960e−002

2/19/6.259000e−003

2/19/6.259000e−003

KOWOSB

4

21/295/3.505040e−002

23/324/3.630220e−002

83/1,077/1.314390e−001

104/1,345/1.664894e−001

BD

4

17/244/3.505040e−002

19/276/3.880580e−002

2/19/7.510800e−003

2/19/1.001440e−002

OSB1

5

2/42/2.128060e−002

2/42/1.877700e−002

2/19/7.510800e−003

2/19/1.001440e−002

BIGGS

6

25/322/4.506480e−002

7/108/2.253240e−002

15/330/4.381300e−002

21/287/4.130940e−002

OSB2

11

3/56/6.259000e−002

3/56/6.259000e−002

3/33/1.877700e−002

3/33/2.002880e−002

WATSON

20

31/457/3.880580e−001

29/412/3.555112e−001

2/19/2.002880e−002

2/19/2.253240e−002

ROSEX

100

229/3,704/1.268073e+000

276/4,359/1.512174e+000

2/19/1.126620e−002

2/19/1.251800e−002

SINGX

400

65/922/1.174939e+001

155/2,375/2.844465e+001

2/19/2.065470e−001

2/19/2.115542e−001

PEN1

400

2/47/7.247922e−001

2/47/7.310512e−001

2/19/1.940290e−001

2/19/1.927772e−001

PEN2

200

2/25/6.884900e−002

2/25/6.634540e−002

2/19/6.008640e−002

2/19/6.384180e−002

VARDIM

100

2/47/2.879140e−002

2/47/2.879140e−002

2/19/1.001440e−002

2/19/8.762600e−003

TRIG

500

9/138/1.627340e+002

9/144/1.671604e+002

8/146/1.700345e+002

50/876/1.039274e+003

BV

500

2/19/3.492522e−001

2/19/3.492522e−001

2/19/3.480004e−001

2/19/3.517558e−001

IE

500

6/71/7.711088e+000

6/71/7.706081e+000

6/71/7.722354e+000

6/71/7.772426e+000

TRID

500

53/760/1.622333e+001

50/727/1.501159e+001

564/7,325/1.690631e+002

564/7,325/1.692333e+002

BAND

500

12/275/5.551733e+000

12/238/4.696754e+000

2/19/4.781876e−001

2/19/4.431372e−001

LIN

500

2/19/4.719286e−001

2/19/4.744322e−001

2/19/4.806912e−001

2/19/4.719286e−001

LIN1

500

3/32/9.363464e−001

3/32/9.388500e−001

3/31/9.050514e−001

3/31/9.025478e−001

LIN0

500

3/32/1.165426e+000

3/32/1.161670e+000

3/31/1.119109e+000

3/31/1.130375e+000

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