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NCVXBQP3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME NCVXBQP3
* Problem :
* *********
* A non-convex bound constrained quadratic program.
* SIF input: Nick Gould, July 1995
* classification QBR2-AN-V-0
* The number of variables
*IE N 10 $-PARAMETER
*IE N 50 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 1000 $-PARAMETER original value
IE N 10000 $-PARAMETER
* Other useful values.
IE 1 1
IE 2 2
IE 3 3
IE 4 4
* The number of equality constraints
I/ M N 2
* 75% positive eigenvalues
I/ NPLUS N 4
I* NPLUS NPLUS 3
IA NPLUS+1 NPLUS 1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
* Objective function groups:
* the i-th group has nonzeros in positions
* i, mod( 2i - 1, n ) + 1 and mod( 3i - 1, n ) + 1
DO I 1 N
XN OBJ(I) X(I) 1.0
IM J I 2
IA J J -1
I/ K J N
I* K K N
I- J J K
IA J J 1
XN OBJ(I) X(J) 1.0
IM J I 3
IA J J -1
I/ K J N
I* K K N
I- J J K
IA J J 1
XN OBJ(I) X(J) 1.0
ND
BOUNDS
DO I 1 N
XL NCVXBQP3 X(I) 0.1
XU NCVXBQP3 X(I) 10.0
ND
START POINT
XV NCVXBQP3 'DEFAULT' 0.5
GROUP TYPE
GV SQR ALPHA
GP SQR P
GROUP USES
* nplus positive rank-one terms
DO I 1 NPLUS
XT OBJ(I) SQR
RI RI I
ZP OBJ(I) P RI
ND
* n - nplus negative rank-one terms
DO I NPLUS+1 N
XT OBJ(I) SQR
RI RI I
RM RI RI -1.0
ZP OBJ(I) P RI
ND
OBJECT BOUND
* Solution
*LO SOLTN -6.60133D+05 $ (n=100)
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
GROUPS NCVXBQP3
INDIVIDUALS
T SQR
F 0.5 * P * ALPHA * ALPHA
G P * ALPHA
H P
ENDATA