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HUMPS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HUMPS
* Problem :
* *********
* A two dimensional function with a lot of humps.
* The density of humps increases with the parameter ZETA,
* making the problem more difficult.
* The problem is nonconvex.
* Source:
* Ph. Toint, private communication, 1997.
* SDIF input: Ph. Toint, May 1997.
* classification SUR2-AN-2-0
* Density of humps
*RE ZETA 2.0
RE ZETA 20.0
VARIABLES
X
Y
GROUPS
N OBJ
BOUNDS
FR HUMPS 'DEFAULT'
START POINT
V HUMPS X -506.0
V HUMPS Y -506.2
ELEMENT TYPE
EV HMP X Y
EP HMP A
EV SQ X
ELEMENT USES
T H HMP
V H X X
V H Y Y
ZP H A ZETA
T SX SQ
V SX X X
T SY SQ
V SY X Y
GROUP USES
E OBJ H 1.0
E OBJ SY 0.05 SX 0.05
OBJECT BOUND
LO HUMPS 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HUMPS
TEMPORARIES
R AA
R AAA
R SAX
R SAY
R CAX
R CAY
M SIN
M COS
INDIVIDUALS
T HMP
A SAX SIN( A * X )
A SAY SIN( A * Y )
A CAX COS( A * X )
A CAY COS( A * Y )
A AA A + A
A AAA A * AA
F ( SAX * SAY )**2
G X AA * SAX * CAX * SAY**2
G Y AA * SAX**2 * CAY * SAY
H X X AAA * SAY**2 * ( CAX**2 - SAX**2 )
H X Y AA * AA * SAX * CAX * SAY * CAY
H Y Y AAA * SAX**2 * ( CAY**2 - SAY**2 )
T SQ
F X**2
G X X + X
H X X 2.0
ENDATA