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Numerical results in Guo's paper (A New Superlinearly Convergent Algorithm of Combining QP Subproblem with System of Linear Equations for Constrained Optimization,submitted to JOTA ) for Figures 1 and 2.  

2011-09-18 20:38:21|  分类: My paper |  标签: |举报 |字号 订阅

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Table 1. Numerical results for Figures 1 and 2. ALGO A is compared with VFO2AD, OPRQP and PTSQP.

Prob

Code

NF0

NDF0

FV

VC

KKT

CPU

012

ALGO A

VFO2AD

OPRQP

PTSQP

8

12

40

7

8

12

26

7

-.30000000E+02

-.30000000E+02

-.30000004E+02

-.30000000E+02

0

0.58E-09

0.76E-05

0.0

0.45E-06

0.35E-07

0.15E-09

0.12E-06

0.03

-

-

-

029

ALGO A

VFO2AD

OPRQP

PTSQP

14

13

64

14

14

13

39

10

-.22627417E+02

-.22627417E+02

-.22627421E+02

-.22627417E+02

0

0.0

0.56E-05

0.0

0.13E-06

0.16E-05

0.10E-05

0.17E-06

0.09

-

-

-

030

ALGO A

VFO2AD

OPRQP

PTSQP

11

14

18

14

11

14

18

13

0.67235378E-19

0.10000000E+01

0.10000000E+01

0.10000000E+01

0

0.0

0.38E-08

0.0

0.52E-09

0.56E-08

0.28E-09

0.0

0.03

-

-

-

031

ALGO A

VFO2AD

OPRQP

PTSQP

10

10

24

11

10

10

22

8

0.60000000E+01

0.60000000E+01

0.59999631E+01

0.60000000E+01

0

0.27E-09

0.62E-05

0.0

0.29E-03

0.12E-04

0.13E-06

0.41E-06

0.08

-

-

-

033

ALGO A

VFO2AD

OPRQP

PTSQP

13

5

43

4

13

5

39

4

-.45857864E+01

-.40000000E+01

-.40000000E+01

-.40000000E+01

0

0.0

0.32E-10

0.0

0.91E-07

0.0

0.0

0.0

0.16

-

-

-

034

ALGO A

VFO2AD

OPRQP

PTSQP

11

8

60

9

11

8

37

8

-.83403245E+00

-.83403245E+00

-.83403515E+00

-.83403245E+00

0

0.15E-08

0.73E-05

0.0

0.65E-06

0.0

0.0

0.43E-08

0.14

-

-

-

043

 

 

 

ALGO A

VFO2AD

OPRQP

PTSQP

13

12

31

9

13

12

24

9

-.44000000E+02

-.44000000E+02

-.44000013E+02

-.44000000E+02

0

0.35E-09

0.79E-05

0.0

0.25E-03

0.75E-05

0.19E-06

0.68E-04

0.09

-

-

-

057

 

 

 

ALGO A

VFO2AD

OPRQP

PTSQP

4

4

40

33

4

4

24

19

0.30646308E-01

0.30646306E-01

0.28459078E-01

0.28459673E-01

0

0.0

0.89E-05

0.0

0.26E-05

0.0

0.89E-06

0.20E-07

0.02

-

-

-

066

 

 

 

ALGO A

VFO2AD

OPRQP

PTSQP

8

7

18

8

8

7

17

8

0.51816327E+00

0.51816327E+00

0.51815751E+00

0.51816324E+00

0

0.39E-08

0.10E-04

0.0

0.67E-07

0.57E-06

0.11E-10

0.0

0.03

-

-

-

084

 

 

 

ALGO A

VFO2AD

OPRQP

PTSQP

34

6

43

4

21

6

5

4

-.52803256E+07

-.52803365E+07

-.55883016E+07

-.52803389E+07

0

0.63E-01

0.68E+00

0.0

0.17E+06

0.0

0.22E+06

0.0

0.36

-

-

-

100

ALGO A

VFO2AD

OPRQP

PTSQP

19

20

49

42

19

20

31

14

0.68011661E+03

0.68063006E+03

0.68063005E+03

0.68063006E+03

0

0.76E-07

0.76E-05

0.0

0.32E-03

0.29E-03

0.73E-08

0.21E-03

0.19

-

-

-

113

ALGO A

VFO2AD

OPRQP

PTSQP

15

15

30

18

15

15

28

14

0.24306209E+02

0.24306209E+02

0.24306193E+02

0.24306209E+02

0

0.16E-0

0.13E-04

0.0

0.16E-03

0.11E-03

0.11E-08

0.17E-04

0.23

-

-

-

117

ALGO A

VFO2AD

OPRQP

PTSQP

18

17

41

28

18

17

40

16

0.32348679E+02

0.32348679E+02

0.32348442E+02

0.32348679E+02

0

0.36E-07

0.54E-05

0.0

0.13E-03

0.28E-05

0.73E-06

0.68E-04

0.45

-

-

-

Notes: ALGO A: Our new algorithm.

      VFO2AD: Reference [12] (Powell, M.J.D.: A fast algorithm for nonlinearly constrained optimization calculations. In: Proceedings of the 1977 Dundee Conference on Numerical Analysis, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, New York(1978) )

      OPRQP: References [35, 36] (Biggs, M.C.: On the convergence of some constrained

minimization algorithms based on recursive quadratic programming. J. Institute Math. Appl. 21, 67-82 (1978) ; Bartholomew-Biggs, M.C.: An improved implementation of the recursive quadratic programming method for constrained minimization. Technical Report 105, Numerical Optimization Centre, The Hatfield Polytechnic, England(1979))

      PTSQP: Reference [3] (Panier, E.R., Tits, A.L.: A superlinearly convergent feasible method for the solution of inequality constrained optimization problems. SIAM J. Control Optim. 25, 934-950 (1987) )  

     NDF0:The number of gradient evaluations of objective function.

     VC:    The sum of constraint violation, given by \sum\limits_{j\in I}\max\{0, f_j(x)\}$ at the final iteration point.

     KKT: The norm of KKT vector, i.e., \|\nabla_xL(x^k,\lambda^k)\|.

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