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HS67.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HS67
* Problem :
* *********
* Source: problem 67 in
* W. Hock and K. Schittkowski,
* "Test examples for nonlinear programming codes",
* Lectures Notes in Economics and Mathematical Systems 187, Springer
* Verlag, Heidelberg, 1981.
* Original Source: problem 8 in
* A.R. Colville
* "A comparative study on nonlinear programming"
* IBM Scientific Center Report 320-2949, New York, 1968.
* SIF input: A.R. Conn & Nick Gould, April 1991.
* classification OOI2-AN-3-14
* Set useful parameters
IE 1 1
IE 2 2
IE 3 3
IE 4 4
IE 5 5
IE 6 6
IE 7 7
IE 8 8
IE 9 9
IE 10 10
IE 11 11
IE 12 12
IE 13 13
IE 14 14
AE A(1) 0.0
AE A(2) 0.0
AE A(3) 85.0
AE A(4) 90.0
AE A(5) 3.0
AE A(6) 0.01
AE A(7) 145.0
AE A(8) 5000.0
AE A(9) 2000.0
AE A(10) 93.0
AE A(11) 95.0
AE A(12) 12.0
AE A(13) 4.0
AE A(14) 162.0
VARIABLES
DO I 1 3
X X(I)
ND
GROUPS
* Objective function
XN OBJ X(1) 5.04 X(2) 0.035
XN OBJ X(3) 10.0
* Constraint functions
DO I 1 7
XG AG(I)
XL AL(I)
ND
CONSTANTS
DO I 1 7
IA I+7 I 7
Z HS67 AG(I) A(I)
Z HS67 AL(I) A(I+7)
ND
BOUNDS
* All variables are in greater than 0.00001
LO HS67 'DEFAULT' 0.00001
XU HS67 X(1) 2000.0
XU HS67 X(2) 16000.0
XU HS67 X(3) 120.0
START POINT
XV HS67 X(1) 1745.0
XV HS67 X(2) 12000.0
XV HS67 X(3) 110.0
ELEMENT TYPE
EV Y2Y5 U1 U2
EV Y2Y5 U3
EV Y2 U1 U2
EV Y2 U3
EV Y3 U1 U2
EV Y3 U3
EV Y4 U1 U2
EV Y4 U3
EV Y5 U1 U2
EV Y5 U3
EV Y6 U1 U2
EV Y6 U3
EV Y7 U1 U2
EV Y7 U3
EV Y8 U1 U2
EV Y8 U3
ELEMENT USES
T E25 Y2Y5
V E25 U1 X1
V E25 U2 X2
V E25 U3 X3
T E2 Y2
V E2 U1 X1
V E2 U2 X2
V E2 U3 X3
T E3 Y3
V E3 U1 X1
V E3 U2 X2
V E3 U3 X3
T E4 Y4
V E4 U1 X1
V E4 U2 X2
V E4 U3 X3
T E5 Y5
V E5 U1 X1
V E5 U2 X2
V E5 U3 X3
T E6 Y6
V E6 U1 X1
V E6 U2 X2
V E6 U3 X3
T E7 Y7
V E7 U1 X1
V E7 U2 X2
V E7 U3 X3
T E8 Y8
V E8 U1 X1
V E8 U2 X2
V E8 U3 X3
GROUP USES
E OBJ E25 -0.063 E3 3.36
XE AG(1) E2
XE AL(1) E2
XE AG(2) E3
XE AL(2) E3
XE AG(3) E4
XE AL(3) E4
XE AG(4) E5
XE AL(4) E5
XE AG(5) E6
XE AL(5) E6
XE AG(6) E7
XE AL(6) E7
XE AG(7) E8
XE AL(7) E8
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HS67
TEMPORARIES
R DUMMY
R HS67
R Y(8)
R G(8,3)
R H(8,6)
L EVAL
F HS67
GLOBALS
A EVAL .FALSE.
INDIVIDUALS
T Y2Y5
E EVAL DUMMY HS67( U1, U2, U3, Y, G, H )
A EVAL .TRUE.
F Y( 2 ) * Y( 5 )
G U1 Y( 2 ) * G( 5, 1 ) +
G+ Y( 5 ) * G( 2, 1 )
G U2 Y( 2 ) * G( 5, 2 ) +
G+ Y( 5 ) * G( 2, 2 )
G U3 Y( 2 ) * G( 5, 3 ) +
G+ Y( 5 ) * G( 2, 3 )
H U1 U1 Y( 2 ) * H( 5, 1 ) +
H+ 2.0 * G( 5, 1 ) * G( 2, 1 ) +
H+ Y( 5 ) * H( 2, 1 )
H U1 U2 Y( 2 ) * H( 5, 2 ) +
H+ G( 5, 1 ) * G( 2, 2 ) +
H+ G( 5, 2 ) * G( 2, 1 ) +
H+ Y( 5 ) * H( 2, 2 )
H U1 U3 Y( 2 ) * H( 5, 3 ) +
H+ G( 5, 1 ) * G( 2, 3 ) +
H+ G( 5, 3 ) * G( 2, 1 ) +
H+ Y( 5 ) * H( 2, 3 )
H U2 U2 Y( 2 ) * H( 5, 4 ) +
H+ 2.0 * G( 5, 2 ) * G( 2, 2 ) +
H+ Y( 5 ) * H( 2, 4 )
H U2 U3 Y( 2 ) * H( 5, 5 ) +
H+ G( 5, 2 ) * G( 2, 3 ) +
H+ G( 5, 3 ) * G( 2, 2 ) +
H+ Y( 5 ) * H( 2, 5 )
H U3 U3 Y( 2 ) * H( 5, 6 ) +
H+ 2.0 * G( 5, 3 ) * G( 2, 3 ) +
H+ Y( 5 ) * H( 2, 6 )
T Y2
E EVAL DUMMY HS67( U1, U2, U3, Y, G, H )
A EVAL .TRUE.
F Y( 2 )
G U1 G( 2, 1 )
G U2 G( 2, 2 )
H U1 U1 H( 2, 1 )
H U2 U1 H( 2, 2 )
H U2 U2 H( 2, 4 )
T Y3
E EVAL DUMMY HS67( U1, U2, U3, Y, G, H )
A EVAL .TRUE.
F Y( 3 )
G U1 G( 3, 1 )
G U2 G( 3, 2 )
H U1 U1 H( 3, 1 )
H U2 U1 H( 3, 2 )
H U2 U2 H( 3, 4 )
T Y4
E EVAL DUMMY HS67( U1, U2, U3, Y, G, H )
A EVAL .TRUE.
F Y( 4 )
G U1 G( 4, 1 )
G U2 G( 4, 2 )
G U3 G( 4, 3 )
H U1 U1 H( 4, 1 )
H U2 U1 H( 4, 2 )
H U3 U1 H( 4, 3 )
H U2 U2 H( 4, 4 )
H U3 U2 H( 4, 5 )
H U3 U3 H( 4, 6 )
T Y5
E EVAL DUMMY HS67( U1, U2, U3, Y, G, H )
A EVAL .TRUE.
F Y( 5 )
G U1 G( 5, 1 )
G U2 G( 5, 2 )
G U3 G( 5, 3 )
H U1 U1 H( 5, 1 )
H U2 U1 H( 5, 2 )
H U3 U1 H( 5, 3 )
H U2 U2 H( 5, 4 )
H U3 U2 H( 5, 5 )
H U3 U3 H( 5, 6 )
T Y6
E EVAL DUMMY HS67( U1, U2, U3, Y, G, H )
A EVAL .TRUE.
F Y( 6 )
G U1 G( 6, 1 )
G U2 G( 6, 2 )
H U1 U1 H( 6, 1 )
H U2 U1 H( 6, 2 )
H U2 U2 H( 6, 4 )
T Y7
E EVAL DUMMY HS67( U1, U2, U3, Y, G, H )
A EVAL .TRUE.
F Y( 7 )
G U1 G( 7, 1 )
G U2 G( 7, 2 )
G U3 G( 7, 3 )
H U1 U1 H( 7, 1 )
H U2 U1 H( 7, 2 )
H U3 U1 H( 7, 3 )
H U2 U2 H( 7, 4 )
H U3 U2 H( 7, 5 )
H U3 U3 H( 7, 6 )
T Y8
E EVAL DUMMY HS67( U1, U2, U3, Y, G, H )
F Y( 8 )
G U1 G( 8, 1 )
G U2 G( 8, 2 )
G U3 G( 8, 3 )
H U1 U1 H( 8, 1 )
H U2 U1 H( 8, 2 )
H U3 U1 H( 8, 3 )
H U2 U2 H( 8, 4 )
H U3 U2 H( 8, 5 )
H U3 U3 H( 8, 6 )
ENDATA
C EXTERNAL PROCEDURE
DOUBLE PRECISION FUNCTION HS67( X1, X2, X3, Y, G, H )
DOUBLE PRECISION X1, X2, X3, Y( 8 ), G( 8, 3 ), H( 8, 6 )
C
C PAGE 129 Hock and Schittkowski.
C
DOUBLE PRECISION Y2C, Y4C, Y2Y7X3
INTRINSIC ABS
HS67 = 0.0
C
C FIRST APPROXIMATION TO Y2.
C
Y( 2 ) = 1.6 * X1
G( 2, 1 ) = 1.6
G( 2, 2 ) = 0.0
G( 2, 3 ) = 0.0
H( 2, 1 ) = 0.0
H( 2, 2 ) = 0.0
H( 2, 3 ) = 0.0
H( 2, 4 ) = 0.0
H( 2, 5 ) = 0.0
H( 2, 6 ) = 0.0
C
C LOOP UNTIL Y2 CONVERGES.
C
10 CONTINUE
C
C Y3.
C
Y( 3 ) = 1.22 * Y( 2 ) - X1
G( 3, 1 ) = 1.22 * G( 2, 1 ) - 1.0
G( 3, 2 ) = 1.22 * G( 2, 2 )
G( 3, 3 ) = 1.22 * G( 2, 3 )
H( 3, 1 ) = 1.22 * H( 2, 1)
H( 3, 2 ) = 1.22 * H( 2, 2)
H( 3, 3 ) = 1.22 * H( 2, 3)
H( 3, 4 ) = 1.22 * H( 2, 4)
H( 3, 5 ) = 1.22 * H( 2, 5)
H( 3, 6 ) = 1.22 * H( 2, 6)
C
C Y6.
C
Y( 6 ) = ( X2 + Y( 3 ) ) / X1
G( 6, 1 ) = - Y( 6 ) / X1 + G( 3, 1 ) / X1
G( 6, 2 ) = 1.0 / X1 + G( 3, 2 ) / X1
G( 6, 3 ) = G( 3, 3 ) / X1
H( 6, 1 ) = - G( 6, 1) / X1 + Y( 6 )/ X1 ** 2 - G( 3, 1 ) /
+ X1 **2 + H( 3, 1) / X1
H( 6, 2 ) = - G( 6, 2 ) / X1 + H( 3, 2 ) / X1
H( 6, 3 ) = - G( 6, 3 ) / X1 + H( 3, 3 ) / X1
H( 6, 4 ) = H( 3, 4 ) / X1
H( 6, 5 ) = H( 3, 5 ) / X1
H( 6, 6 ) = H( 3, 6 ) / X1
Y2C = 0.01 * X1 * ( 112.0 + 13.167 * Y( 6 ) - 0.6667 *
+ Y( 6 ) ** 2 )
IF ( ABS( Y2C - Y( 2 ) ) .GT. 0.001 ) THEN
C
C Y2.
C
Y( 2 ) = Y2C
G( 2, 1) = 0.01 * ( 112.0 + 13.167 * Y( 6 ) - 0.6667 *
+ Y( 6 ) ** 2 ) + X1 * 0.13167 * G( 6, 1 ) -
+ X1 * 0.013334 * Y( 6) * G( 6, 1 )
G( 2, 2) = X1 * ( 0.13167 * G( 6, 2 ) - 0.013334 * Y( 6) *
+ G( 6, 2) )
G( 2, 3) = X1 * ( 0.13167 * G( 6, 3 ) - 0.013334 * Y( 6) *
+ G( 6, 3) )
H( 2, 1 ) = 0.13167 * G( 6, 1 ) - 0.013334 * Y( 6) *
+ G( 6, 1 ) + 0.13167 * G( 6, 1 ) - 0.013334 *
+ Y( 6) * G( 6, 1 ) + X1 * 0.13167 * H( 6, 1 ) -
+ X1 * 0.013334 * G( 6, 1 ) ** 2 - X1 * 0.013334 *
+ Y( 6 ) * H( 6, 1 )
H( 2, 2 ) = 0.13167 * G( 6, 2 ) - 0.013334 * Y( 6) *
+ G( 6, 2 ) + X1 * 0.13167 * H( 6, 2 ) -
+ X1 * 0.013334 * G( 6, 2 ) * G( 6, 1 ) - X1 *
+ 0.013334 * Y( 6 ) * H( 6, 2 )
H( 2, 3 ) = 0.13167 * G( 6, 3 ) - 0.013334 * Y( 6) *
+ G( 6, 3 ) + X1 * 0.13167 * H( 6, 3 ) -
+ X1 * 0.013334 * G( 6, 3 ) * G( 6, 1 ) - X1 *
+ 0.013334 * Y( 6 ) * H( 6, 3 )
H( 2, 4 ) = X1 * ( 0.13167 * H( 6, 4 ) - 0.013334 * G( 6, 2 )
+ ** 2 - 0.013334 * Y( 6) * H( 6, 4 ))
H( 2, 5 ) = X1 * ( 0.13167 * H( 6, 5 ) - 0.013334 * G( 6, 3 )
+ * G( 6, 2 ) - 0.013334 * Y( 6) * H( 6, 5 ))
H( 2, 6 ) = X1 * ( 0.13167 * H( 6, 6 ) - 0.013334 * G( 6, 3 )
+ ** 2 - 0.013334 * Y( 6) * H( 6, 6 ))
GO TO 10
END IF
C
C FIRST APPROXIMATION TO Y4.
C
Y( 4 ) = 93.0
G( 4, 1 ) = 0.0
G( 4, 2 ) = 0.0
G( 4, 3 ) = 0.0
H( 4, 1 ) = 0.0
H( 4, 2 ) = 0.0
H( 4, 3 ) = 0.0
H( 4, 4 ) = 0.0
H( 4, 5 ) = 0.0
H( 4, 6 ) = 0.0
C
C LOOP UNTIL Y4 CONVERGES.
C
40 CONTINUE
C
C Y5.
C
Y( 5 ) = 86.35 + 1.098 * Y( 6 ) - 0.038 * Y( 6) ** 2 +
+ 0.325 * ( Y( 4 ) - 89.0 )
G( 5, 1 ) = 1.098 * G( 6, 1 ) - 0.076 * Y( 6 ) * G( 6, 1) +
+ 0.325 * G( 4, 1 )
G( 5, 2 ) = 1.098 * G( 6, 2 ) - 0.076 * Y( 6 ) * G( 6, 2) +
+ 0.325 * G( 4, 2 )
G( 5, 3 ) = 1.098 * G( 6, 3 ) - 0.076 * Y( 6 ) * G( 6, 3) +
+ 0.325 * G( 4, 3 )
H( 5, 1 ) = 1.098 * H( 6, 1 ) - 0.076 * G( 6, 1 ) * G( 6, 1 )
* - 0.076 * Y( 6 ) * H( 6, 1 ) + 0.325 * H( 4, 1 )
H( 5, 2 ) = 1.098 * H( 6, 2 ) - 0.076 * G( 6, 1 ) * G( 6, 2 )
* - 0.076 * Y( 6 ) * H( 6, 2 ) + 0.325 * H( 4, 2 )
H( 5, 3 ) = 1.098 * H( 6, 3 ) - 0.076 * G( 6, 1 ) * G( 6, 3 )
* - 0.076 * Y( 6 ) * H( 6, 3 ) + 0.325 * H( 4, 3 )
H( 5, 4 ) = 1.098 * H( 6, 4 ) - 0.076 * G( 6, 2 ) * G( 6, 2 )
* - 0.076 * Y( 6 ) * H( 6, 4 ) + 0.325 * H( 4, 4 )
H( 5, 5 ) = 1.098 * H( 6, 5 ) - 0.076 * G( 6, 2 ) * G( 6, 3 )
* - 0.076 * Y( 6 ) * H( 6, 5 ) + 0.325 * H( 4, 5 )
H( 5, 6 ) = 1.098 * H( 6, 6 ) - 0.076 * G( 6, 3 ) * G( 6, 3 )
* - 0.076 * Y( 6 ) * H( 6, 6 ) + 0.325 * H( 4, 6 )
C
C Y8.
C
Y( 8 ) = 3.0 * Y( 5 ) - 133.0
G( 8, 1 ) = 3.0 * G( 5, 1 )
G( 8, 2 ) = 3.0 * G( 5, 2 )
G( 8, 3 ) = 3.0 * G( 5, 3 )
H( 8, 1 ) = 3.0 * H( 5, 1 )
H( 8, 2 ) = 3.0 * H( 5, 2 )
H( 8, 3 ) = 3.0 * H( 5, 3 )
H( 8, 4 ) = 3.0 * H( 5, 4 )
H( 8, 5 ) = 3.0 * H( 5, 5 )
H( 8, 6 ) = 3.0 * H( 5, 6 )
C
C Y3.
C
Y( 7 ) = 35.82 - 0.222 * Y( 8 )
G( 7, 1 ) = - 0.222 * G( 8, 1 )
G( 7, 2 ) = - 0.222 * G( 8, 2 )
G( 7, 3 ) = - 0.222 * G( 8, 3 )
H( 7, 1 ) = - 0.222 * H( 8, 1 )
H( 7, 2 ) = - 0.222 * H( 8, 2 )
H( 7, 3 ) = - 0.222 * H( 8, 3 )
H( 7, 4 ) = - 0.222 * H( 8, 4 )
H( 7, 5 ) = - 0.222 * H( 8, 5 )
H( 7, 6 ) = - 0.222 * H( 8, 6 )
Y2Y7X3 = Y( 2 ) * Y( 7 ) + 1000.0 * X3
Y4C = 98000.0 * X3 / Y2Y7X3
IF ( ABS( Y4C - Y( 4 ) ) .GT. 0.001 ) THEN
C
C Y4.
C
Y( 4 ) = Y4C
G( 4, 1 ) = - 98000.0 * X3 * ( G( 2, 1 ) * Y( 7 ) + Y( 2 ) *
+ G( 7, 1) ) / Y2Y7X3 ** 2
G( 4, 2 ) = - 98000.0 * X3 * ( G( 2, 2 ) * Y( 7 ) + Y( 2 ) *
+ G( 7, 2) ) / Y2Y7X3 ** 2
G( 4, 3 ) = 98000.0 / Y2Y7X3
+ - 98000.0 * X3 * ( G( 2, 3 ) * Y( 7 ) + Y( 2 ) *
+ G( 7, 3) + 1000.0 ) / Y2Y7X3 ** 2
H( 4, 1 ) = - 98000.0 * X3 * ( H( 2, 1 ) * Y( 7 ) +
+ 2.0 * G( 2, 1 ) * G( 7, 1 ) + Y( 2 ) *
+ H( 7, 1 ) ) / Y2Y7X3 ** 2
+ + 196000.0 * X3 * ( G( 2, 1 ) * Y( 7 )
+ + Y( 2 ) * G( 7, 1) ) ** 2 / Y2Y7X3 ** 3
H( 4, 2 ) = - 98000.0 * X3 * ( H( 2, 2 ) * Y( 7 ) + G( 2, 2 )
+ * G( 7, 1 ) + G( 2, 1 ) * G( 7, 2 ) + Y( 2 ) *
+ H( 7, 2) ) / Y2Y7X3 ** 2
+ + 196000.0 * X3 * ( G( 2, 2 ) * Y( 7 )
+ + Y( 2 ) * G( 7, 2) ) * ( G( 2, 1 ) * Y( 7 )
+ + Y( 2 ) * G( 7, 1 ) ) / Y2Y7X3 ** 3
H( 4, 3 ) = - 98000.0 * ( Y( 2 ) * G( 7, 1 ) + Y( 7 ) *
+ G( 2, 1 ) ) / Y2Y7X3 ** 2
+ - 98000.0 * X3 * ( G( 2, 3 ) * G( 7, 1 ) +
+ Y( 2 ) * H( 7, 3 ) + G( 2, 1 ) * G( 7, 3 ) +
+ H( 2, 3 ) * Y( 7 ) ) / Y2Y7X3 ** 2 +
+ 196000.0 * X3 * ( Y( 2 ) * G( 7, 1 ) + Y( 7 ) *
+ G( 2, 1 ) ) * ( G( 2, 3 ) * Y( 7 ) + Y( 2 ) *
+ G( 7, 3 ) + 1000.0 ) / Y2Y7X3 ** 3
H( 4, 4 ) = - 98000.0 * X3 * ( H( 2, 4 ) * Y( 7 ) +
+ 2.0 * G( 2, 2 ) * G( 7, 2 ) + Y( 2 ) *
+ H( 7, 4) ) / Y2Y7X3 ** 2
+ + 196000.0 * X3 * ( G( 2, 2 ) * Y( 7 )
+ + Y( 2 ) * G( 7, 2) ) ** 2 / Y2Y7X3 ** 3
H( 4, 5 ) = - 98000.0 * ( Y( 2 ) * G( 7, 2 ) + Y( 7 ) *
+ G( 2, 2 ) ) / Y2Y7X3 ** 2
+ - 98000.0 * X3 * ( G( 2, 3 ) * G( 7, 2 ) +
+ Y( 2 ) * H( 7, 5 ) + G( 2, 2 ) * G( 7, 3 ) +
+ H( 2, 5 ) * Y( 7 ) ) / Y2Y7X3 ** 2 +
+ 196000.0 * X3 * ( Y( 2 ) * G( 7, 2 ) + Y( 7 ) *
+ G( 2, 2 ) ) * ( G( 2, 3 ) * Y( 7 ) + Y( 2 ) *
+ G( 7, 3 ) + 1000.0 ) / Y2Y7X3 ** 3
H( 4, 6 ) = - 196000.0 * ( Y( 2 ) * G( 7, 3 ) + Y( 7 ) *
+ G( 2, 3 ) + 1000.0 ) / Y2Y7X3 ** 2
+ - 98000.0 * X3 *
+ ( H( 2, 6 ) * Y( 7 ) + 2.0 * G( 2, 3 ) *
+ G( 7, 3 ) + Y( 2 ) * H( 7, 6 ) ) / Y2Y7X3 ** 2
+ + 196000.0 * X3 * ( G( 2, 3 ) * Y( 7 ) + Y( 2 )
+ * G( 7, 3 ) + 1000.0 ) ** 2 / Y2Y7X3 ** 3
GO TO 40
END IF
RETURN
END