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GOULDQP3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME GOULDQP3
* Problem :
* *********
* Source: a variant on a problem of optimal knot placement in a
* scheme for ordinary differential equations with boundary values
* suggested by J. R. Kightley, see N. I. M. Gould, "An algorithm for
* large-scale quadratic programming", IMA J. Num. Anal (1991),
* 11, 299-324, problem class 3. Note that the optimal solution values
* given in that paper are incorrect.
* SIF input: Nick Gould, December 1991
* Revised June 1998 with rescaling for larger examples
* classification QLR2-MN-V-V
* Number of knots
*IE K 50 $-PARAMETER
*IE K 100 $-PARAMETER
*IE K 150 $-PARAMETER
*IE K 200 $-PARAMETER
*IE K 250 $-PARAMETER
*IE K 300 $-PARAMETER
*IE K 350 $-PARAMETER original value
*IE K 1000 $-PARAMETER
*IE K 5000 $-PARAMETER
IE K 10000 $-PARAMETER
*IE K 50001 $-PARAMETER
* Other useful parameters
IA K+1 K 1
IA K-1 K -1
IA K-2 K -2
IE 1 1
IE 2 2
* Minimum knot spacings
IE 1000 1000
I/ K/1000 K 1000
IM I2 K/1000 2
IA I+1 K/1000 1
I/ K>1000 I2 I+1
IS K<1000 K>1000 1
RI RK<1000 K<1000
RI RK>1000 K>1000
RM FACT1 RK<1000 1.01
RM FACT2 RK>1000 1.0001
R+ FACTOR FACT1 FACT2
RE ALPHA 1.0
R= BETA FACTOR
RE A1 2.0
DO I 2 K+1
A+ A(I) ALPHA BETA
A* BETA BETA FACTOR
ND
VARIABLES
DO I 1 K
X KNOT(I)
ND
DO I 1 K-1
X SPACE(I)
ND
GROUPS
DO I 1 K-2
IA I+1 I 1
XN OBJ1(I) SPACE(I+1)1.0 SPACE(I) -1.0
ND
DO I 1 K-1
I- K-I K I
XN OBJ2(I) KNOT(K-I) 1.0 SPACE(I) 1.0
ND
DO I 1 K-1
IA I+1 I 1
XE CON(I) SPACE(I) 1.0
XE CON(I) KNOT(I+1) -1.0 KNOT(I) 1.0
ND
CONSTANTS
DO I 1 K-1
I- J K+1 I
Z GOULDQP3 OBJ2(I) A(J)
ND
BOUNDS
DO I 1 K
IA I+1 I 1
ZL GOULDQP3 KNOT(I) A(I)
ZU GOULDQP3 KNOT(I) A(I+1)
ND
DO I 1 K-1
IA I+2 I 2
A- DIF A(I+2) A(I)
AM DIFL DIF 0.4
AM DIFU DIF 0.6
ZL GOULDQP3 SPACE(I) DIFL
ZU GOULDQP3 SPACE(I) DIFU
ND
START POINT
DO I 1 K
Z GOULDQP3 KNOT(I) A(I)
ND
DO I 1 K-1
IA I+1 I 1
A- DIF A(I+1) A(I)
Z GOULDQP3 SPACE(I) DIF
ND
GROUP TYPE
GV SQUARE ALPHA
GROUP USES
DO I 1 K-2
XT OBJ1(I) SQUARE
ND
DO I 1 K-1
XT OBJ2(I) SQUARE
ND
OBJECT BOUND
LO GOULDQP3 0.0
* Solution
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
GROUPS GOULDQP3
INDIVIDUALS
T SQUARE
F 5.0D-1 * ALPHA * ALPHA
G ALPHA
H 1.0D+0
ENDATA