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HS54.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HS54
* Problem :
* *********
* Source: problem 54, incorrectly stated in
* W. Hock and K. Schittkowski,
* "Test examples for nonlinear programming codes",
* Lectures Notes in Economics and Mathematical Systems 187, Springer
* Verlag, Heidelberg, 1981.
* Betts problem 11.7, JOTA 21, 1977, pp.137-174.
* SIF input: A.R. Conn, April 1990 and Nick Gould, October 1990
* classification OLR2-AN-6-1
* some useful parameters, including N, the number of variables.
IE N 6
IE 1 1
IE 6 6
RE RHO 2.0D-1
R* RHOSQR RHO RHO
RS 1-RHOSQR RHOSQR 1.0
RD FACTOR 1-RHOSQR 1.0
RE MU1 1.0D+4
RE MU2 1.0D+0
RE MU3 2.0D+6
RE MU4 1.0D+1
RE MU5 1.0D-3
RE MU6 1.0D+8
RE SIGMA1 8.0D+3
RE SIGMA2 1.0D+0
RE SIGMA3 7.0D+6
RE SIGMA4 5.0D+1
RE SIGMA5 5.0D-2
RE SIGMA6 5.0D+8
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
N OBJ
E CON1 X1 1.0 X2 4.0D+3
CONSTANTS
RM 0.2SI1 SIGMA1 2.0D-1
RM 2000SI2 SIGMA2 2.0D+3
RM 4000MU2 MU2 4.0D+3
R+ RHS MU1 4000MU2
R+ RHS RHS 0.2SI1
R+ RHS RHS 2000SI2
Z HS54 CON1 RHS
BOUNDS
UP HS54 X1 2.0D+4
LO HS54 X2 - 1.0D+1
UP HS54 X2 1.0D+1
UP HS54 X3 1.0D+7
UP HS54 X4 2.0D+1
LO HS54 X5 - 1.0D+0
UP HS54 X5 1.0D+0
UP HS54 X6 2.0D+8
START POINT
HS54 X1 6.0D+3
HS54 X2 1.5D+0
HS54 X3 4.0D+6
HS54 X4 2.0D+0
HS54 X5 3.0D-3
HS54 X6 5.0D+7
ELEMENT TYPE
EV SQR V1
EP SQR MU SIGMA
EV PROD V1 V2
EP PROD MU1 MU2
EP PROD SIGMA1 SIGMA2
EP PROD RHO
ELEMENT USES
XT 'DEFAULT' SQR
DO I 1 6
ZV E(I) V1 X(I)
ZP E(I) MU MU(I)
ZP E(I) SIGMA SIGMA(I)
ND
T F1 PROD
V F1 V1 X1
V F1 V2 X2
ZP F1 RHO RHO
ZP F1 MU1 MU1
ZP F1 MU2 MU2
ZP F1 SIGMA1 SIGMA1
ZP F1 SIGMA2 SIGMA2
GROUP TYPE
GV NORMAL Q
GROUP USES
T OBJ NORMAL
ZE OBJ E1 FACTOR
ZE OBJ E2 FACTOR
E OBJ E3 1.0D+0 E4 1.0D+0
E OBJ E5 1.0D+0 E6 1.0D+0
ZE OBJ F1 FACTOR
OBJECT BOUND
* Solution
*LO SOLTN 0.90807482
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HS54
TEMPORARIES
R V1MP
R TERM1
R TERM2
R RHO2
INDIVIDUALS
T SQR
A V1MP ( V1 - MU ) / SIGMA
F V1MP ** 2
G V1 2.0 * V1MP / SIGMA
H V1 V1 2.0 / SIGMA ** 2
T PROD
A TERM1 ( V1 - MU1 ) / SIGMA1
A TERM2 ( V2 - MU2 ) / SIGMA2
A RHO2 RHO + RHO
F RHO2 * TERM1 * TERM2
G V1 RHO2 * TERM2 / SIGMA1
G V2 RHO2 * TERM1 / SIGMA2
H V1 V2 RHO2 / ( SIGMA1 * SIGMA2 )
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS HS54
TEMPORARIES
R EXPHV
M EXP
INDIVIDUALS
T NORMAL
A EXPHV EXP( - 0.5 * Q )
F - EXPHV
G 5.0D-1 * EXPHV
H - 2.5D-1 * EXPHV
ENDATA