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LUKVLI1.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME LUKVLI1
* Problem :
* *********
* Source: Problem 5.1, the chained Rosenbrock function with
* simplified trigonometric exponential 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
IA N-1 N -1
IA N-2 N -2
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N-1
IA I+1 I 1
XN Q(I) 'SCALE' 0.01
XN Q(I) X(I+1) -1.0
XN L(I) X(I) 1.0
ND
DO K 1 N-2
IA K+1 K 1
IA K+2 K 2
XL C(K) X(K+2) 2.0 X(K+1) 4.0
ND
CONSTANTS
DO I 1 N-1
X RHS L(I) 1.0
ND
DO K 1 N-2
X RHS C(K) 8.0
ND
BOUNDS
FR LUKVLI1 'DEFAULT'
START POINT
DO I 1 N
DI I 2
XV LUKVLI1 X(I) -1.2
ND
DO I 2 N
DI I 2
XV LUKVLI1 X(I) 1.0
ND
ELEMENT TYPE
EV SQR V
EV CUBE V
EV XEXP X1 X2
EV SINASINB X1 X2
ELEMENT USES
DO I 1 N-1
XT Q(I) SQR
ZV Q(I) V X(I)
ND
DO K 1 N-2
IA K+1 K 1
IA K+2 K 2
XT CA(K) CUBE
ZV CA(K) V X(K+1)
XT CB(K) SINASINB
ZV CB(K) X1 X(K+1)
ZV CB(K) X2 X(K+2)
XT CC(K) XEXP
ZV CC(K) X1 X(K)
ZV CC(K) X2 X(K+1)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
DO I 1 N-1
XT Q(I) L2
XE Q(I) Q(I)
XT L(I) L2
ND
DO K 1 N-2
XE C(K) CA(K) 3.0 CB(K)
XE C(K) CC(K) -1.0
ND
OBJECT BOUND
LO LUKVLI1 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS LUKVLI1
TEMPORARIES
R EXPX
R XEXPX
R SINA
R SINB
R COSA
R COSB
M EXP
M SIN
M COS
INDIVIDUALS
T SQR
F V ** 2
G V 2.0 * V
H V V 2.0
T XEXP
A EXPX EXP( X1 - X2 )
A XEXPX X1 * EXPX
F XEXPX
G X1 EXPX + XEXPX
G X2 - XEXPX
H X1 X1 2.0 * EXPX + XEXPX
H X1 X2 - EXPX - XEXPX
H X2 X2 XEXPX
T SINASINB
A SINA SIN( X1 - X2 )
A SINB SIN( X1 + X2 )
A COSA COS( X1 - X2 )
A COSB COS( X1 + X2 )
F SINA * SINB
G X1 SINA * COSB + COSA * SINB
G X2 SINA * COSB - COSA * SINB
H X1 X1 2.0 * ( COSA * COSB - SINA * SINB )
H X2 X2 - 2.0 * ( COSA * COSB + SINA * SINB )
T CUBE
F V ** 3
G V 3.0 * V ** 2
H V V 6.0 * V
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS LUKVLI1
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA