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CRAGGLVY.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME CRAGGLVY
* Problem :
* *********
* Extended Cragg and Levy problem.
* This problem is a sum of m sets of 5 groups,
* There are 2m+2 variables. The Hessian matrix is 7-diagonal.
* Source: problem 32 in
* Ph. L. Toint,
* "Test problems for partially separable optimization and results
* for the routine PSPMIN",
* Report 83/4, Department of Mathematics, FUNDP (Namur, B), 1983.
* See also Buckley#18
* SIF input: Ph. Toint, Dec 1989.
* classification OUR2-AY-V-0
* M is the number of group sets
*IE M 1 $-PARAMETER n = 4 original value
*IE M 4 $-PARAMETER n = 10
*IE M 24 $-PARAMETER n = 50
*IE M 49 $-PARAMETER n = 100
*IE M 249 $-PARAMETER n = 500
*IE M 499 $-PARAMETER n = 1000
IE M 2499 $-PARAMETER n = 5000
* N is the number of variables
IM 2M M 2
IA N 2M 2
* Define useful parameters
IE 1 1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 M
IM 2I I 2
IA 2I-1 2I -1
IA 2I+1 2I 1
IA 2I+2 2I 2
XN A(I) X(2I) -1.0
XN B(I) 'SCALE' 0.01
XN B(I) X(2I) 1.0 X(2I+1) -1.0
XN C(I) X(2I+1) 1.0 X(2I+2) -1.0
XN D(I) X(2I-1) 1.0
XN F(I) X(2I+2) 1.0
ND
CONSTANTS
DO I 1 M
X CRAGGLVY F(I) 1.0
ND
BOUNDS
FR CRAGGLVY 'DEFAULT'
START POINT
XV CRAGGLVY 'DEFAULT' 2.0
X CRAGGLVY X(1) 1.0
ELEMENT TYPE
EV EXPN V
EV TANG V1 V2
IV TANG U
ELEMENT USES
DO I 1 M
IM 2I I 2
IA 2I-1 2I -1
IA 2I+1 2I 1
IA 2I+2 2I 2
XT AE(I) EXPN
ZV AE(I) V X(2I-1)
XT CE(I) TANG
ZV CE(I) V1 X(2I+1)
ZV CE(I) V2 X(2I+2)
ND
GROUP TYPE
GV L2 GVAR
GV L4 GVAR
GV L6 GVAR
GV L8 GVAR
GROUP USES
DO I 1 M
XT A(I) L4
XE A(I) AE(I)
XT B(I) L6
XT C(I) L4
XE C(I) CE(I)
XT D(I) L8
XT F(I) L2
ND
OBJECT BOUND
LO CRAGGLVY 0.0
* Solution
*LO SOLTN(2) 0.0
*LO SOLTN(4) 1.886566
*LO SOLTN(24) 1.5372D+01
*LO SOLTN(29) 3.2270D+01
*LO SOLTN(249) 1.6745D+02
*LO SOLTN(499) 3.3642D+02
*LO SOLTN(2499) 1.6882D+03
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS CRAGGLVY
TEMPORARIES
R FVAL
R SECU
R SECUSQ
R TANU
M EXP
M TAN
M COS
INDIVIDUALS
* Exponential
T EXPN
A FVAL EXP( V )
F FVAL
G V FVAL
H V V FVAL
* Tangent
T TANG
R U V1 1.0 V2 -1.0
A TANU TAN( U )
A SECU 1.0 / COS( U )
A SECUSQ SECU * SECU
F TANU
G U SECUSQ
H U U 2.0 * SECUSQ * TANU
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS CRAGGLVY
INDIVIDUALS
* Least-square groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
* Least fourth power
T L4
F GVAR**4
G 4.0 * GVAR**3
H 12.0 * GVAR**2
* Least sixth power groups
T L6
F GVAR**6
G 6.0 * GVAR**5
H 30.0 * GVAR**4
* Least eighth power
T L8
F GVAR**8
G 8.0 * GVAR**7
H 56.0 * GVAR**6
ENDATA