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DIXMAANF.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DIXMAANF
* Problem :
* *********
* The Dixon-Maany test problem (version F)
* Source:
* L.C.W. Dixon and Z. Maany,
* "A family of test problems with sparse Hessians for unconstrained
* optimization",
* TR 206, Numerical Optimization Centre, Hatfield Polytechnic, 1988.
* See also Buckley#221 (p. 49)
* SIF input: Ph. Toint, Dec 1989.
* correction by Ph. Shott, January 1995.
* classification OUR2-AN-V-0
* M is equal to the third of the number of variables
*IE M 5 $-PARAMETER n = 15 original value
*IE M 30 $-PARAMETER n = 90
*IE M 100 $-PARAMETER n = 300
*IE M 500 $-PARAMETER n = 1500
IE M 1000 $-PARAMETER n = 3000
*IE M 3000 $-PARAMETER n = 9000
* N is the number of variables
IM N M 3
* Problem parameters
RE ALPHA 1.0
RE BETA 0.0625
RE GAMMA 0.0625
RE DELTA 0.0625
* K-set 2
IE K1 1
IE K2 0
IE K3 0
IE K4 1
* Other parameters
RI RN N
IA N-1 N -1
I+ 2M M M
IE 1 1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
N GA
N GB
N GC
N GD
CONSTANTS
DIXMAANF GA -1.0
BOUNDS
FR DIXMAANF 'DEFAULT'
START POINT
XV DIXMAANF 'DEFAULT' 2.0
ELEMENT TYPE
EV SQ X
EV SQB X Y
EV SQC X Y
EV 2PR X Y
ELEMENT USES
* First group
DO I 1 N
XT A(I) SQ
ZV A(I) X X(I)
ND
* Second group
DO I 1 N-1
IA I+1 I 1
XT B(I) SQB
ZV B(I) X X(I)
ZV B(I) Y X(I+1)
ND
* Third group
DO I 1 2M
I+ I+M I M
XT C(I) SQC
ZV C(I) X X(I)
ZV C(I) Y X(I+M)
ND
* Fourth group
DO I 1 M
I+ I+2M I 2M
XT D(I) 2PR
ZV D(I) X X(I)
ZV D(I) Y X(I+2M)
ND
GROUP USES
* First group
DO I 1 N
RI RI I
R/ I/N RI RN
RE TMP 1.0
DO J 1 K1
R* TMP TMP I/N
OD J
R* AI TMP ALPHA
ZE GA A(I) AI
ND
* Second group
DO I 1 N-1
RI RI I
R/ I/N RI RN
RE TMP 1.0
DO J 1 K2
R* TMP TMP I/N
OD J
R* BI TMP BETA
ZE GB B(I) BI
ND
* Third group
DO I 1 2M
RI RI I
R/ I/N RI RN
RE TMP 1.0
DO J 1 K3
R* TMP TMP I/N
OD J
R* CI TMP GAMMA
ZE GC C(I) CI
ND
* Fourth group
DO I 1 M
RI RI I
R/ I/N RI RN
RE TMP 1.0
DO J 1 K4
R* TMP TMP I/N
OD J
R* DI TMP DELTA
ZE GD D(I) DI
ND
OBJECT BOUND
LO DIXMAANF 0.0
* Solution
*LO SOLTN 1.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DIXMAANF
TEMPORARIES
R F1
R F2
R DF2DY
INDIVIDUALS
* First type
T SQ
F X * X
G X X + X
H X X 2.0
* Second type
T SQB
A F1 X * X
A F2 Y + Y * Y
A DF2DY 1.0 + 2.0 * Y
F F1 * F2 * F2
G X 2.0 * X * F2 * F2
G Y 2.0 * F1 * F2 * DF2DY
H X X 2.0 * F2 * F2
H X Y 4.0 * X * DF2DY * F2
H Y Y 4.0 * F1 * F2 +
H+ 2.0 * F1 * DF2DY * DF2DY
* Third type
T SQC
A F1 X * X
A F2 Y**4
F F1 * F2
G X 2.0 * X * F2
G Y 4.0 * F1 * Y**3
H X X 2.0 * F2
H X Y 8.0 * X * Y**3
H Y Y 12.0 * F1 * Y**2
* Fourth type
T 2PR
F X * Y
G X Y
G Y X
H X Y 1.0
ENDATA