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LUKVLE3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME LUKVLE3
* Problem :
* *********
* Source: Problem 5.3, the chained Powell singular 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
* 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-1 N -1
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 OA(I) X(2I-1) 1.0 X(2I) 10.0
XN OB(I) X(2I+1) 1.0 X(2I+2) -1.0
XN OC(I) X(2I) 1.0 X(2I+1) -2.0
XN OD(I) X(2I-1) 1.0 X(2I+2) -1.0
ND
XE C1 X(2) 2.0
XE C2 X(N-1) 4.0
CONSTANTS
X RHS C1 5.0
X RHS C2 3.0
BOUNDS
FR LUKVLE3 'DEFAULT'
START POINT
DO I 1 N
DI I 4
XV LUKVLE3 X(I) 3.0
ND
DO I 2 N
DI I 4
XV LUKVLE3 X(I) -1.0
ND
DO I 3 N
DI I 4
XV LUKVLE3 X(I) 0.0
ND
DO I 4 N
DI I 4
XV LUKVLE3 X(I) 1.0
ND
ELEMENT TYPE
EV CUBE V
EV XEXP X1 X2
EV SINASINB X1 X2
ELEMENT USES
XT C11 CUBE
ZV C11 V X(1)
XT C12 SINASINB
ZV C12 X1 X(1)
ZV C12 X2 X(2)
XT C21 XEXP
ZV C21 X1 X(N-1)
ZV C21 X2 X(N)
GROUP TYPE
GV L2P GVAR
GP L2P P
GV L4P GVAR
GP L4P P
GROUP USES
DO I 1 N/2-1
XT OA(I) L2P
XP OA(I) P 1.0
XT OB(I) L2P
XP OB(I) P 5.0
XT OC(I) L4P
XP OC(I) P 1.0
XT OD(I) L4P
XP OD(I) P 10.0
ND
XE C1 C11 3.0 C12
XE C2 C21 -1.0
OBJECT BOUND
LO LUKVLE3 0.0
* Solution
*LO SOLTN 2.758658E+01
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS LUKVLE3
TEMPORARIES
R EXPX
R XEXPX
R SINA
R SINB
R COSA
R COSB
M EXP
M SIN
M COS
INDIVIDUALS
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 LUKVLE3
INDIVIDUALS
T L2P
F P * GVAR * GVAR
G 2.0 * P * GVAR
H 2.0 * P
T L4P
F P * GVAR ** 4
G 4.0 * P * GVAR ** 3
H 12.0 * P * GVAR ** 2
ENDATA