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LUKVLE7.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME LUKVLE7
* Problem :
* *********
* Source: Problem 5.7, A trigonometric tridiagonal function with
* simplified five-diagonal 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
* 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
IA N-1 N -1
IA N-2 N -2
IA N-3 N -3
RI N N
RM -N N -1.0
RA N+1 N 1.0
R* N.N+1 N N+1
RM -N.N+1/2 N.N+1 -0.5
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
XN OBJ
XE C(1) X(1) 4.0 X(2) 1.0
XE C(2) X(2) 6.0 X(3) 1.0
XE C(3) X(N-1) 6.0 X(N-3) -1.0
XE C(4) X(N) 2.0 X(N-2) -1.0
CONSTANTS
Z RHS OBJ -N.N+1/2
X RHS C(2) 2.0
X RHS C(3) 2.0
BOUNDS
FR BND 'DEFAULT'
START POINT
DO I 1 N
XV LUKVLE7 X(I) 1.0
ND
ELEMENT TYPE
EV SIN V
EV COS V
EV SQR V
EV CUBEP V W
ELEMENT USES
DO I 1 N
XT SI(I) SIN
ZV SI(I) V X(I)
XT CO(I) COS
ZV CO(I) V X(I)
ND
XT C1(1) SQR
ZV C1(1) V X(2)
XT C2(1) SQR
ZV C2(1) V X(3)
XT C1(2) CUBEP
ZV C1(2) V X(2)
ZV C1(2) W X(1)
XT C2(2) SQR
ZV C2(2) V X(3)
XT C3(2) SQR
ZV C3(2) V X(4)
XT C1(3) CUBEP
ZV C1(3) V X(N-1)
ZV C1(3) W X(N-2)
XT C2(3) SQR
ZV C2(3) V X(N)
XT C3(3) SQR
ZV C3(3) V X(N-2)
XT C1(4) CUBEP
ZV C1(4) V X(N)
ZV C1(4) W X(N-1)
XT C2(4) SQR
ZV C2(4) V X(N-1)
GROUP USES
XE OBJ CO(1) -1.0
XE OBJ SI(2) -1.0
DO I 2 N-1
IA I+1 I 1
IA I-1 I -1
RI I I
RM -I I -1.0
ZE OBJ CO(I) -I
ZE OBJ SI(I-1) I
ZE OBJ SI(I+1) -I
ND
ZE OBJ CO(N) -N
ZE OBJ SI(N-1) N
XE C(1) C1(1) -4.0
XE C(1) C2(1) -1.0
XE C(2) C1(2) 8.0
XE C(2) C2(2) -4.0
XE C(2) C3(2) -1.0
XE C(3) C1(3) 8.0
XE C(3) C2(3) -4.0
XE C(3) C3(3) 1.0
XE C(4) C1(4) 8.0
XE C(4) C2(4) 1.0
OBJECT BOUND
LO LUKVLE7 0.0
* Solution
*LO SOLTN -2.2421E+02
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS LUKVLE7
TEMPORARIES
M SIN
M COS
R SINV
R COSV
INDIVIDUALS
T SIN
A SINV SIN( V )
F SINV
G V COS( V )
H V V - SINV
T COS
A COSV COS( V )
F COSV
G V - SIN( V )
H V V - COSV
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