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NCVXQP8.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME NCVXQP8
* Problem :
* *********
* A non-convex quadratic program.
* SIF input: Nick Gould, April 1995
* classification QLR2-AN-V-V
* The number of variables constraints
*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 4
I* M M 3
* 50% positive eigenvalues
I/ NPLUS N 2
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
* linear constraints:
* the i-th constraint has nonzeros in positions
* i, mod( 4i - 1, n ) + 1 and mod( 5i - 1, n ) + 1
DO I 1 M
XE CON(I) X(I) 1.0
IM J I 4
IA J J -1
I/ K J N
I* K K N
I- J J K
IA J J 1
XE CON(I) X(J) 2.0
IM J I 5
IA J J -1
I/ K J N
I* K K N
I- J J K
IA J J 1
XE CON(I) X(J) 3.0
ND
CONSTANTS
DO I 1 M
XE NCVXQP8 CON(I) 6.0
ND
BOUNDS
DO I 1 N
XL NCVXQP8 X(I) 0.1
XU NCVXQP8 X(I) 10.0
ND
START POINT
XV NCVXQP8 '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 -3.04886D+07 $ (n=1000)
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
GROUPS NCVXQP8
INDIVIDUALS
T SQR
F 0.5 * P * ALPHA * ALPHA
G P * ALPHA
H P
ENDATA