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MEXHAT.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME MEXHAT
* Problem :
* *********
* The mexican hat problem with penalty parameter 0.00001
* Source:
* A.A. Brown and M. Bartholomew-Biggs,
* "Some effective methods for unconstrained optimization based on
* the solution of ordinary differential equations",
* Technical Report 178, Numerical Optimization Centre, Hatfield
* Polytechnic, (Hatfield, UK), 1987.
* SIF input: Ph. Toint, June 1990.
* classification OUR2-AN-2-0
* Penalty parameter
RE INVP 0.00001
VARIABLES
X1
X2
GROUPS
N F
ZN C 'SCALE' INVP
CONSTANTS
MEXHAT C 0.02
BOUNDS
FR MEXHAT 'DEFAULT'
START POINT
MEXHAT X1 0.86
MEXHAT X2 0.72
ELEMENT TYPE
EV SSQ X
EP SSQ S
EV XMYSQ X Y
ELEMENT USES
T O1 SSQ
V O1 X X1
P O1 S 1.0
T O2 SSQ
V O2 X X1
P O2 S 1.0
T C1 XMYSQ
V C1 X X2
V C1 Y X1
GROUP TYPE
GV L2 GVAR
GROUP USES
E F O1 -1.0 O2 -1.0
T C L2
E C C1 10000.0 O1
OBJECT BOUND
* Solution
*LO SOLTN -0.0898793
*LO SOLTN -1.1171526
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS MEXHAT
TEMPORARIES
R XMS
R XX
INDIVIDUALS
T SSQ
A XMS X - S
F XMS * XMS
G X XMS + XMS
H X X 2.0
T XMYSQ
A XX X - Y * Y
F XX * XX
G X XX + XX
G Y - 4.0 * XX * Y
H X X 2.0
H X Y - 4.0 * Y
H Y Y - 4.0 * ( XX - 2.0 * Y * Y )
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS MEXHAT
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA