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LUKVLI4.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME LUKVLI4
* Problem :
* *********
* Source: Problem 5.4, the chained Cragg and Levy problem with
* tridiagonal constraints, due to L. Luksan and J. Vlcek,
* "Sparse and partially separable test problems for
* unconstrained and equality constrained optimization",
* Technical Report 767, Inst. Computer Science, Academy of Sciences
* of the Czech Republic, 182 07 Prague, Czech Republic, 1999
* Equality constraints changed to inequalities
* SIF input: Nick Gould, April 2001
* classification OOR2-AY-V-V
* some useful parameters, including N, the number of variables.
*IE N 100 $-PARAMETER
*IE N 1000 $-PARAMETER
IE N 10000 $-PARAMETER
*IE N 100000 $-PARAMETER
* other useful parameters
IE 1 1
IE 2 2
IE 3 3
IE 4 4
IE 5 5
IE 6 6
I/ N/2 N 2
IA N/2-1 N/2 -1
IA N-2 N -2
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N/2-1
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) 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
DO K 1 N-2
IA K+1 K 1
XL C(K) X(K+1) 6.0
ND
CONSTANTS
DO I 1 N/2-1
X RHS F(I) 1.0
ND
DO K 1 N-2
X RHS C(K) 2.0
ND
BOUNDS
FR LUKVLI4 'DEFAULT'
START POINT
*XV START 'DEFAULT' 1.0
DO I 1 N
DI I 4
XV LUKVLI4 X(I) 1.0
ND
DO I 2 N
DI I 4
XV LUKVLI4 X(I) 2.0
ND
DO I 3 N
DI I 4
XV LUKVLI4 X(I) 2.0
ND
DO I 4 N
DI I 4
XV LUKVLI4 X(I) 2.0
ND
ELEMENT TYPE
EV EXPN V
EV TANG V1 V2
IV TANG U
EV SQR V
EV CUBEP V W
ELEMENT USES
DO I 1 N/2-1
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
DO K 1 N-2
IA K+1 K 1
IA K+2 K 2
XT CA(K) CUBEP
ZV CA(K) V X(K+1)
ZV CA(K) W X(K)
XT CB(K) SQR
ZV CB(K) V X(K+2)
ND
GROUP TYPE
GV L2 GVAR
GV L4 GVAR
GV AL6 GVAR
GV L8 GVAR
GROUP USES
DO I 1 N/2-1
XT A(I) L4
XE A(I) AE(I)
XT B(I) AL6
XT C(I) L4
XE C(I) CE(I)
XT D(I) L8
XT F(I) L2
ND
DO K 1 N-2
XE C(K) CA(K) 8.0 CB(K) -4.0
ND
OBJECT BOUND
LO LUKVLI4 0.0
* Solution
*LO SOLTN 4.78473E+03
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS LUKVLI4
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
T SQR
F V * V
G V 2.0 * V
H V V 2.0
T CUBEP
F V ** 3 - V * W
G V 3.0 * V ** 2 - W
G W - V
H V V 6.0 * V
H V W - 1.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS LUKVLI4
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
* Scaled least sixth power groups
T AL6
F 100.0 * GVAR**6
G 600.0 * GVAR**5
H 3000.0 * GVAR**4
* Least eighth power
T L8
F GVAR**8
G 8.0 * GVAR**7
H 56.0 * GVAR**6
ENDATA