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SINEALI.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME SINEALI
* Problem :
* --------
* A variation on the extended Rosenbrock function in which
* the squares are replaced by sines. Bounds are imposed on the
* variables to avoid multiple minima.
* Source: an original idea by
* Ali Bouriacha, private communication.
* SIF input: Nick Gould and Ph. Toint, October, 1993.
* classification OBR2-AN-V-0
* Number of variables
*IE N 4 $-PARAMETER
*IE N 10 $-PARAMETER original value
*IE N 20 $-PARAMETER
*IE N 100 $-PARAMETER
IE N 1000 $-PARAMETER
* other parameter definitions
RE PI 3.1415926535
RM PI/2 PI 0.5
RM 2PI PI 2.0
IE 1 1
IE 2 2
IA N-1 N -1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
N SQ1 X1 1.0
DO I 2 N
XN SQ(I) X(I) 1.0
XN SQ(I) 'SCALE' 0.01
ND
CONSTANTS
SINEALI SQ1 1.0
BOUNDS
RM UB PI 0.5
ZU SINEALI X1 UB
R- LB UB 2PI
ZL SINEALI X1 LB
DO I 2 N
R+ UB1 UB PI/2
R( UB SQRT UB1
ZU SINEALI X(I) UB
R- LB UB 2PI
ZL SINEALI X(I) LB
OD I
START POINT
XV SINEALI 'DEFAULT' 0.0
ELEMENT TYPE
EV ETYPE V1
ELEMENT USES
XT 'DEFAULT' ETYPE
DO I 1 N-1
ZV XSQ(I) V1 X(I)
ND
GROUP TYPE
GV SIN GVAR
GROUP USES
XT 'DEFAULT' SIN
DO I 2 N
IA I-1 I -1
XE SQ(I) XSQ(I-1) -1.0
ND
OBJECT BOUND
* Solution = - 100 * ( N - 1 ) - 1
*LO SOLTN(4) -301.0
*LO SOLTN(10) -901.0
*LO SOLTN(20) -1901.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS SINEALI
INDIVIDUALS
T ETYPE
F V1 * V1
G V1 2.0 * V1
H V1 V1 2.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS SINEALI
TEMPORARIES
R SING
M SIN
M COS
INDIVIDUALS
T SIN
A SING SIN( GVAR )
F SING
G COS( GVAR )
H - SING
ENDATA