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LUKVLE8.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME LUKVLE8
* Problem :
* *********
* Source: Problem 5.8, the augmented Lagrangian function with
* discrete boundard value 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
RE LAMBDA1 -0.002008
RE LAMBDA2 -0.001900
RE LAMBDA3 -0.000261
* other useful parameters
IE 1 1
IE 2 2
IE 3 3
IE 4 4
IE 5 5
RE ONE 1.0
I/ N/5 N 5
IA N-2 N -2
IA N+1 N 1
RI N+1 N+1
R/ H ONE N+1
R* H**2 H H
RM H**2/2 H**2 0.5
RA LAMBA1+10 LAMBDA1 10.0
RA LAMBA3-1 LAMBDA3 -1.0
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N/5
XN O1(I)
XN O2(I)
XN O3(I)
XN O4(I)
ND
DO K 1 N-2
IA K+1 K 1
IA K+2 K 2
XE C(K) X(K+1) 2.0 X(K) -1.0
XE C(K) X(K+2) -1.0
ND
CONSTANTS
DO I 1 N/5
Z RHS O2(I) LAMBA1+10
Z RHS O3(I) LAMBDA2
Z RHS O4(I) LAMBA3-1
ND
BOUNDS
FR LUKVLE8 'DEFAULT'
START POINT
*XV START 'DEFAULT' 1.0
DO I 1 N
DI I 2
XV LUKVLE8 X(I) -1.0
ND
DO I 2 N
DI I 2
XV LUKVLE8 X(I) 2.0
ND
ELEMENT TYPE
EV SQR V
EV SHIFTSQR V
EP SHIFTSQR P
EV CUBE V
EV PROD V W
EV 5PR V1 V2
EV 5PR V3 V4
EV 5PR V5
ELEMENT USES
DO I 1 N/5
IM 5I I 5
IA 5I-1 5I -1
IA 5I-2 5I -2
IA 5I-3 5I -3
IA 5I-4 5I -4
XT O1(I) 5PR
ZV O1(I) V1 X(5I)
ZV O1(I) V2 X(5I-1)
ZV O1(I) V3 X(5I-2)
ZV O1(I) V4 X(5I-3)
ZV O1(I) V5 X(5I-4)
XT O2A(I) SQR
ZV O2A(I) V X(5I)
XT O2B(I) SQR
ZV O2B(I) V X(5I-1)
XT O2C(I) SQR
ZV O2C(I) V X(5I-2)
XT O2D(I) SQR
ZV O2D(I) V X(5I-3)
XT O2E(I) SQR
ZV O2E(I) V X(5I-4)
XT O3A(I) PROD
ZV O3A(I) V X(5I-3)
ZV O3A(I) W X(5I-2)
XT O3B(I) PROD
ZV O3B(I) V X(5I-1)
ZV O3B(I) W X(5I)
XT O4A(I) CUBE
ZV O4A(I) V X(5I-4)
XT O4B(I) CUBE
ZV O4B(I) V X(5I-3)
ND
DO K 1 N-2
IA K+1 K 1
RI K+1 K+1
R* H(K+1) H K+1
RA H.K+1)+1 H(K+1) 1.0
XT C(K) SHIFTSQR
ZV C(K) V X(K+1)
ZP C(K) P H.K+1)+1
ND
GROUP TYPE
GV EXP GVAR
GV 10L2 GVAR
GROUP USES
DO I 1 N/5
XT O1(I) EXP
XE O1(I) O1(I)
XT O2(I) 10L2
XE O2(I) O2A(I) O2B(I)
XE O2(I) O2C(I) O2D(I)
XE O2(I) O2E(I)
XT O3(I) 10L2
XE O3(I) O3A(I) 1.0 O3B(I) -5.0
XT O4(I) 10L2
XE O4(I) O4A(I) O4B(I)
ND
DO K 1 N-2
ZE C(K) C(K) H**2/2
ND
OBJECT BOUND
LO LUKVLE8 0.0
* Solution
*LO SOLTN 8.25936E+04
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS LUKVLE8
TEMPORARIES
R FVAL
R SECU
R SECUSQ
R TANU
M EXP
M TAN
M COS
INDIVIDUALS
T SQR
F V * V
G V 2.0 * V
H V V 2.0
T SHIFTSQR
F ( V + P ) ** 2
G V 2.0 * ( V + P )
H V V 2.0
T CUBE
F V ** 3
G V 3.0 * V ** 2
H V V 6.0 * V
T PROD
F V * W
G V W
G W V
H V W 1.0
T 5PR
F V1 * V2 * V3 * V4 * V5
G V1 V2 * V3 * V4 * V5
G V2 V1 * V3 * V4 * V5
G V3 V1 * V2 * V4 * V5
G V4 V1 * V2 * V3 * V5
G V5 V1 * V2 * V3 * V4
H V1 V2 V3 * V4 * V5
H V1 V3 V2 * V4 * V5
H V1 V4 V2 * V3 * V5
H V1 V5 V2 * V3 * V4
H V2 V3 V1 * V4 * V5
H V2 V4 V1 * V3 * V5
H V2 V5 V1 * V3 * V4
H V3 V4 V1 * V2 * V5
H V3 V5 V1 * V2 * V4
H V4 V5 V1 * V2 * V3
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS LUKVLE8
TEMPORARIES
M EXP
R EXPG
INDIVIDUALS
T EXP
A EXPG EXP( GVAR )
F EXPG
G EXPG
H EXPG
T 10L2
F 10.0 * GVAR * GVAR
G 20.0 * GVAR
H 20.0
ENDATA