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NONCVXU2.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME NONCVXU2
* Problem :
* *********
* A nonconvex unconstrained function with a unique minimum value
* SIF input: Nick Gould, April 1996
* classification OUR2-AN-V-0
* The number of variables
*IE N 10 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 1000 $-PARAMETER original value
IE N 5000 $-PARAMETER
*IE N 10000 $-PARAMETER
* Other useful values.
IA N-1 N -1
IE -1 -1
IE 1 1
IE 2 2
IE 4 4
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
* Objective function groups:
XN OBJ
BOUNDS
XR NONCVXU2 'DEFAULT'
START POINT
DO I 1 N
RI RI I
ZV NONCVXU2 X(I) RI
ND
ELEMENT TYPE
EV SQ V1 V2
EV SQ V3
IV SQ V
EV COS V1 V2
EV COS V3
IV COS V
ELEMENT USES
* the i-th square and cosine elements have nonzeros in positions
* i, mod( 3i - 2, n ) + 1 and mod( 7i - 3, n ) + 1
DO I 1 N
XT SQ(I) SQ
XT COS(I) COS
ZV SQ(I) V1 X(I)
ZV COS(I) V1 X(I)
IM J I 3
IA J J -2
I/ K J N
I* K K N
I- J J K
IA J J 1
ZV SQ(I) V2 X(J)
ZV COS(I) V2 X(J)
IM J I 7
IA J J -3
I/ K J N
I* K K N
I- J J K
IA J J 1
ZV SQ(I) V3 X(J)
ZV COS(I) V3 X(J)
ND
GROUP USES
* n positive rank-one terms
DO I 1 N
XE OBJ SQ(I) COS(I)
ND
OBJECT BOUND
* Solution
*LO SOLUTION 2.3168084D+1 $ (n=10)
*LO SOLUTION 2.3226637D+2 $ (n=100)
*LO SOLUTION 2.3178668D+3 $ (n=1000)
*LO SOLUTION 2.3168368D+4 $ (n=10000)
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS NONCVXU2
TEMPORARIES
R COSV
M COS
M SIN
INDIVIDUALS
T SQ
R V V1 1.0 V2 1.0
R V V3 1.0
F V * V
G V V + V
H V V 2.0
T COS
R V V1 1.0 V2 1.0
R V V3 1.0
A COSV 4.0 * COS( V )
F COSV
G V - 4.0 * SIN( V )
H V V - COSV
ENDATA