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BLOCKQP5.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME BLOCKQP5
* Problem :
* *********
* A nearly degenerate, non-convex quadratic program with some structure.
* The objective function is of the form
*
* sum (i=1,n) (i/n) ( x_i y_i ) + sum(j=1,b) z_j^2
*
* (cf BLOCKQP1.SIF where the factor (i/n) is missing).
* There are n equality constraints of the form
*
* x_i + y_i + sum (j=1,b) z_j = b
*
* There is an inequality constraint of the form
*
* sum(i=1,n) x_i + y_i + sum(j=1,b) z_j >= b + 1
*
* Finally, there are simple bounds
*
* 1 <= x_i, y_i <= 1 (i=1,n)
* 0 <= z_j <= 1 (j=1,b)
*
* (cf BLOCKQP3.SIF where the constraint 0 <= z_j <= 2)
* SIF input: Nick Gould, June 1994
* classification QLR2-AN-V-V
* The number of equality constraints
*IE N 10 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 1000 $-PARAMETER original value
IE N 5000 $-PARAMETER
*IE N 10000 $-PARAMETER
* The number of block-variables
*IE B 5 $-PARAMETER original value
IE B 10 $-PARAMETER
*IE B 50 $-PARAMETER
* Other useful values.
IE 1 1
RI RB B
RA RB+1 RB 1
RI RN N
VARIABLES
DO I 1 N
X X(I)
X Y(I)
ND
DO J 1 B
X Z(J)
ND
GROUPS
N OBJ
DO I 1 N
XG I X(I) 1.0 Y(I) 1.0
XE E(I) X(I) 1.0 Y(I) 1.0
ND
DO J 1 B
XG I Z(J) 1.0
DO I 1 N
XE E(I) Z(J) 1.0
ND
CONSTANTS
DO I 1 N
ZE BLOCKQP5 E(I) RB
ND
ZE BLOCKQP5 I RB+1
BOUNDS
DO I 1 N
XL BLOCKQP5 X(I) -1.0
XU BLOCKQP5 X(I) 1.0
XL BLOCKQP5 Y(I) -1.0
XU BLOCKQP5 Y(I) 1.0
ND
DO J 1 B
XL BLOCKQP5 Z(J) 0.0
XU BLOCKQP5 Z(J) 1.0
ND
START POINT
XV BLOCKQP5 'DEFAULT' 0.5
ELEMENT TYPE
EV SQ Z
EV PROD X Y
ELEMENT USES
DO I 1 N
XT P(I) PROD
ZV P(I) X X(I)
ZV P(I) Y Y(I)
ND
DO I 1 B
XT S(I) SQ
ZV S(I) Z Z(I)
ND
GROUP USES
DO I 1 N
RI RI I
R/ I/N RI RN
ZE OBJ P(I) I/N
ND
DO J 1 B
XE OBJ S(J)
ND
OBJECT BOUND
* Solution
*LO SOLTN -2.4987D-1 $ (n=10,b=5)
*LO SOLTN -4.75D+1 $ (n=100,b=5)
*LO SOLTN -4.975D+2 $ (n=1000,b=5)
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS BLOCKQP5
INDIVIDUALS
T SQ
F 0.5 * Z * Z
G Z Z
H Z Z 1.0
T PROD
F X * Y
G X Y
G Y X
H X Y 1.0
ENDATA