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HS99.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HS99
* Problem :
* *********
* Source: problem 99 in
* W. Hock and K. Schittkowski,
* "Test examples for nonlinear programming codes",
* Lectures Notes in Economics and Mathematical Systems 187, Springer
* Verlag, Heidelberg, 1981.
* SIF input: Ph. Toint, April 1991.
* classification OOR2-AN-7-2
* Constants
IE 1 1
IE 2 2
IE 7 7
IE 8 8
VARIABLES
DO I 1 7
X X(I)
ND
GROUPS
XN OBJ 'SCALE' -1.0
XE Q8E
XE S8E
CONSTANTS
X HS99 Q8E 100000.0
X HS99 S8E 1000.0
BOUNDS
XU HS99 'DEFAULT' 1.58
START POINT
XV HS99 'DEFAULT' 0.5
ELEMENT TYPE
EV R8T X1 X2
EV R8T X3 X4
EV R8T X5 X6
EV R8T X7
EV Q8T X1 X2
EV Q8T X3 X4
EV Q8T X5 X6
EV Q8T X7
EV S8T X1 X2
EV S8T X3 X4
EV S8T X5 X6
EV S8T X7
ELEMENT USES
T R8 R8T
ZV R8 X1 X1
ZV R8 X2 X2
ZV R8 X3 X3
ZV R8 X4 X4
ZV R8 X5 X5
ZV R8 X6 X6
ZV R8 X7 X7
T Q8 Q8T
ZV Q8 X1 X1
ZV Q8 X2 X2
ZV Q8 X3 X3
ZV Q8 X4 X4
ZV Q8 X5 X5
ZV Q8 X6 X6
ZV Q8 X7 X7
T S8 S8T
ZV S8 X1 X1
ZV S8 X2 X2
ZV S8 X3 X3
ZV S8 X4 X4
ZV S8 X5 X5
ZV S8 X6 X6
ZV S8 X7 X7
GROUP TYPE
GV L2 GVAR
GROUP USES
T OBJ L2
XE OBJ R8
XE Q8E Q8
XE S8E S8
OBJECT BOUND
* Solution
*LO SOLTN -831079892.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HS99
TEMPORARIES
R A2
R A3
R A4
R A5
R A6
R A7
R A8
R DT2
R DT3
R DT4
R DT5
R DT6
R DT7
R DT8
R B
R R2
R R3
R R4
R R5
R R6
R R7
R S2
R S3
R S4
R S5
R S6
R S7
R DSD1
R DSD2
R DSD3
R DSD4
R DSD5
R DSD6
R DSD7
R D2SD1
R D2SD2
R D2SD3
R D2SD4
R D2SD5
R D2SD6
R D2SD7
R Q2
R Q3
R Q4
R Q5
R Q6
R Q7
M SIN
M COS
GLOBALS
A A2 50.0
A A3 50.0
A A4 75.0
A A5 75.0
A A6 75.0
A A7 100.0
A A8 100.0
A DT2 25.0
A DT3 25.0
A DT4 50.0
A DT5 50.0
A DT6 50.0
A DT7 90.0
A DT8 90.0
A B 32.0
INDIVIDUALS
T R8T
A R2 A2 * DT2 * COS( X1 )
A R3 A3 * DT3 * COS( X2 ) + R2
A R4 A4 * DT4 * COS( X3 ) + R3
A R5 A5 * DT5 * COS( X4 ) + R4
A R6 A6 * DT6 * COS( X5 ) + R5
A R7 A7 * DT7 * COS( X6 ) + R6
F A8 * DT8 * COS( X7 ) + R7
G X1 - A2 * DT2 * SIN( X1 )
G X2 - A3 * DT3 * SIN( X2 )
G X3 - A4 * DT4 * SIN( X3 )
G X4 - A5 * DT5 * SIN( X4 )
G X5 - A6 * DT6 * SIN( X5 )
G X6 - A7 * DT7 * SIN( X6 )
G X7 - A8 * DT8 * SIN( X7 )
H X1 X1 - A2 * DT2 * COS( X1 )
H X2 X2 - A3 * DT3 * COS( X2 )
H X3 X3 - A4 * DT4 * COS( X3 )
H X4 X4 - A5 * DT5 * COS( X4 )
H X5 X5 - A6 * DT6 * COS( X5 )
H X6 X6 - A7 * DT7 * COS( X6 )
H X7 X7 - A8 * DT8 * COS( X7 )
T S8T
A S2 DT2 * ( A2 * SIN( X1 ) - B )
A S3 DT3 * ( A3 * SIN( X2 ) - B ) + S2
A S4 DT4 * ( A4 * SIN( X3 ) - B ) + S3
A S5 DT5 * ( A5 * SIN( X4 ) - B ) + S4
A S6 DT6 * ( A6 * SIN( X5 ) - B ) + S5
A S7 DT7 * ( A7 * SIN( X6 ) - B ) + S6
F DT8 * ( A8 * SIN( X7 ) - B ) + S7
G X1 A2 * DT2 * COS( X1 )
G X2 A3 * DT3 * COS( X2 )
G X3 A4 * DT4 * COS( X3 )
G X4 A5 * DT5 * COS( X4 )
G X5 A6 * DT6 * COS( X5 )
G X6 A7 * DT7 * COS( X6 )
G X7 A8 * DT8 * COS( X7 )
H X1 X1 - A2 * DT2 * SIN( X1 )
H X2 X2 - A3 * DT3 * SIN( X2 )
H X3 X3 - A4 * DT4 * SIN( X3 )
H X4 X4 - A5 * DT5 * SIN( X4 )
H X5 X5 - A6 * DT6 * SIN( X5 )
H X6 X6 - A7 * DT7 * SIN( X6 )
H X7 X7 - A8 * DT8 * SIN( X7 )
T Q8T
A S2 DT2 * ( A2 * SIN( X1 ) - B )
A S3 DT3 * ( A3 * SIN( X2 ) - B ) + S2
A S4 DT4 * ( A4 * SIN( X3 ) - B ) + S3
A S5 DT5 * ( A5 * SIN( X4 ) - B ) + S4
A S6 DT6 * ( A6 * SIN( X5 ) - B ) + S5
A S7 DT7 * ( A7 * SIN( X6 ) - B ) + S6
A DSD1 A2 * DT2 * COS( X1 )
A DSD2 A3 * DT3 * COS( X2 )
A DSD3 A4 * DT4 * COS( X3 )
A DSD4 A5 * DT5 * COS( X4 )
A DSD5 A6 * DT6 * COS( X5 )
A DSD6 A7 * DT7 * COS( X6 )
A DSD7 A8 * DT8 * COS( X7 )
A D2SD1 - A2 * DT2 * SIN( X1 )
A D2SD2 - A3 * DT3 * SIN( X2 )
A D2SD3 - A4 * DT4 * SIN( X3 )
A D2SD4 - A5 * DT5 * SIN( X4 )
A D2SD5 - A6 * DT6 * SIN( X5 )
A D2SD6 - A7 * DT7 * SIN( X6 )
A D2SD7 - A8 * DT8 * SIN( X7 )
A Q2 0.5 * DT2 * DT2 * ( A2 * SIN( X1) - B )
A Q3 0.5 * DT3 * DT3 * ( A3 * SIN( X2) - B )
A+ + DT3 * S2 + Q2
A Q4 0.5 * DT4 * DT4 * ( A4 * SIN( X3) - B )
A+ + DT4 * S3 + Q3
A Q5 0.5 * DT5 * DT5 * ( A5 * SIN( X4) - B )
A+ + DT5 * S4 + Q4
A Q6 0.5 * DT6 * DT6 * ( A6 * SIN( X5) - B )
A+ + DT6 * S5 + Q5
A Q7 0.5 * DT7 * DT7 * ( A7 * SIN( X6) - B )
A+ + DT7 * S6 + Q6
F 0.5 * DT8 * DT8 * ( A8 * SIN( X7) - B )
F+ + DT8 * S7 + Q7
G X1 0.5 * DT2 * DT2 * A2 * COS( X1 )
G+ + (DT8+DT7+DT6+DT5+DT4+DT3) * DSD1
G X2 0.5 * DT3 * DT3 * A3 * COS( X2 )
G+ + (DT8+DT7+DT6+DT5+DT4) * DSD2
G X3 0.5 * DT4 * DT4 * A4 * COS( X3 )
G+ + (DT8+DT7+DT6+DT5) * DSD3
G X4 0.5 * DT5 * DT5 * A5 * COS( X4 )
G+ + (DT8+DT7+DT6) * DSD4
G X5 0.5 * DT6 * DT6 * A6 * COS( X5 )
G+ + (DT8+DT7) * DSD5
G X6 0.5 * DT7 * DT7 * A7 * COS( X6 )
G+ + DT8 * DSD6
G X7 0.5 * DT8 * DT8 * A8 * COS( X7 )
H X1 X1 - 0.5 * DT2 * DT2 * A2 * SIN( X1 )
H+ + (DT8+DT7+DT6+DT5+DT4+DT3) * D2SD1
H X2 X2 - 0.5 * DT3 * DT3 * A3 * SIN( X2 )
H+ + (DT8+DT7+DT6+DT5+DT4) * D2SD2
H X3 X3 - 0.5 * DT4 * DT4 * A4 * SIN( X3 )
H+ + (DT8+DT7+DT6+DT5) * D2SD3
H X4 X4 - 0.5 * DT5 * DT5 * A5 * SIN( X4 )
H+ + (DT8+DT7+DT6) * D2SD4
H X5 X5 - 0.5 * DT6 * DT6 * A6 * SIN( X5 )
H+ + (DT8+DT7) * D2SD5
H X6 X6 - 0.5 * DT7 * DT7 * A7 * SIN( X6 )
H+ + DT8 * D2SD6
H X7 X7 - 0.5 * DT8 * DT8 * A8 * SIN( X7 )
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS HS99
* Least-square groups
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA