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HS110.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HS110
* Problem :
* *********
* This problem is a sum of 2n+1 groups, 2n of which contain 1 linear
* element and the other one contains n elements.
* Source: problem 110 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: A.R. Conn, Mar 1990.
* classification SBR2-AN-V-0
* N is the number of variables
IE N 10 $-PARAMETER original value
*IE N 50 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 200 $-PARAMETER
* Define useful parameters
IE 1 1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N
XN 2LOG(I) X(I) 1.0
XN 10LOG(I) X(I) -1.0
ND
N GEXP
CONSTANTS
DO I 1 N
X HS110 2LOG(I) 2.0
X HS110 10LOG(I) -10.0
ND
BOUNDS
XL HS110 'DEFAULT' 2.001
XU HS110 'DEFAULT' 9.999
START POINT
XV HS110 'DEFAULT' 9.0
ELEMENT TYPE
EV LOG X
ELEMENT USES
DO I 1 N
XT LOGX(I) LOG
ZV LOGX(I) X X(I)
ND
GROUP TYPE
GV LOGSQR GVAR
GV EXP GVAR
GROUP USES
XT 'DEFAULT' LOGSQR
T GEXP EXP
DO I 1 N
XE GEXP LOGX(I)
ND
OBJECT BOUND
* Solution
*LO SOLTN -45.77846971
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HS110
TEMPORARIES
M LOG
INDIVIDUALS
* Logarithmic elements
T LOG
F LOG(X)
G X 1.0/X
H X X -1.0/X**2
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS HS110
TEMPORARIES
M LOG
M EXP
R LOGVAR
R EXPVAR
INDIVIDUALS
T LOGSQR
A LOGVAR LOG(GVAR)
F LOGVAR**2
G 2.0*LOGVAR/GVAR
H 2.0*(1.0 - LOGVAR)/GVAR**2
T EXP
A EXPVAR -EXP(0.2*GVAR)
F EXPVAR
G 0.2*EXPVAR
H 0.04*EXPVAR
ENDATA