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DEGENQP.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DEGENQP
* Problem :
* *********
* A simple degenerate convex quadratic program,
* with a large number of constraints
* SIF input: Nick Gould, February 2000
* classification QLR2-AN-V-V
* Number of variables. NB: there will be O(N**3) constraints
*IE N 10 $-PARAMETER
*IE N 20 $-PARAMETER original value
IE N 50 $-PARAMETER
* Other useful parameters
IE 1 1
IE 2 2
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
* objective function
DO I 1 N
XN OBJ X(I) 1.0
ND
* constraints
DO I 1 N
DI I 2
IE I+1 I 1
XE E(I) X(I) 1.0 X(I+1) -1.0
ND
DO I 1 N
IE I+1 I 1
DO J I+1 N
IE J+1 J 1
DO K J+1 N
XG C(I,J,K) X(I) 1.0 X(J) 1.0
XG C(I,J,K) X(K)
ND
CONSTANTS
X DEGENQP 'DEFAULT' 0.0
RANGES
X DEGENQP 'DEFAULT' 2.0
BOUNDS
LO DEGENQP 'DEFAULT' 0.0
UP DEGENQP 'DEFAULT' 1.0
START POINT
DEGENQP 'DEFAULT' 2.0
ELEMENT TYPE
EV SQUARE ALPHA
ELEMENT USES
DO I 1 N
XT O(I) SQUARE
ZV O(I) ALPHA X(I)
ND
GROUP USES
RI RN N
DO I 1 N
RI RI I
R/ RI/RN RI RN
ZE OBJ O(I) RI/RN
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DEGENQP
INDIVIDUALS
T SQUARE
F 5.0D-1 * ALPHA * ALPHA
G ALPHA ALPHA
H ALPHA ALPHA 1.0D+0
ENDATA