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JANNSON3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME JANNSON3
* Problem :
* *********
* Source: example 3 in
* C. Jannson
* "Convex-concave extensions"
* BIT 40(2) 2000:291-313
* SIF input: Nick Gould, September 2000
* classification OQR2-AN-V-3
*IE N 3 $-PARAMETER
IE N 10000 $-PARAMETER
* Other parameters
IE 0 0
IE 1 1
IE 2 2
IM 2N N 2
IM 5N N 5
RE 1.0 1.0
RI 5RN 5N
R/ 1/5N 1.0 5RN
VARIABLES
DO I 1 2N
X X(I)
ND
GROUPS
XN G X2 -1.0
XN G0 X1 1.0
DO I 1 2N
XN G(I) X(I) 1.0
XE L X(I) 1.0
ND
XL Q
XL P
CONSTANTS
X JANNSON3 G0 1.0
DO I 1 2N
X JANNSON3 G(I) 1.0
ND
X JANNSON3 L 1.0
X JANNSON3 Q 0.75
Z JANNSON3 P 1/5N
BOUNDS
LO JANNSON3 'DEFAULT' -1.0
UP JANNSON3 'DEFAULT' 1.0
ELEMENT TYPE
EV SQR X
EV PROD X Y
ELEMENT USES
DO I 1 2N
XT E(I) SQR
ZV E(I) X X(I)
ND
DO I 1 N
I+ N+I N I
XT P(I) PROD
ZV P(I) X X(I)
ZV P(I) Y X(N+I)
ND
GROUP TYPE
GV L2 GVAR
GV L22 GVAR
GROUP USES
XT G L22
XE G E(1)
DO I 0 2N
XT G(I) L2
ND
DO I 1 2N
XE Q E(I)
ND
DO I 1 N
XE P P(I)
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO JANNSON3 0.0
* Solution
*XL SOLUTION 1.99985D+04 $ n = 10000
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS JANNSON3
INDIVIDUALS
T SQR
F X * X
G X X + X
H X X 2.0
T PROD
F X * Y
G X Y
G Y X
H X Y 1.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS JANNSON3
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
T L22
F 0.5 * GVAR * GVAR
G GVAR
H 1.0
ENDATA