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MADSEN.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME MADSEN
* Problem :
* *********
* A nonlinear minmax problem.
* Source:
* K. Madsen
* "An algorithm for minmax solution of overdetermined systems of non-linear
* equations"
* JIMA, vol.16, pp. 321-328, 1975.
* SIF input: Ph. Toint, April 1992.
* classification LOR2-AN-3-6
VARIABLES
X1
X2
U
GROUPS
XN OBJ U 1.0
XG C1 U 1.0
XG C2 U 1.0
XG C3 U 1.0
XG C4 U 1.0
XG C5 U 1.0
XG C6 U 1.0
BOUNDS
FR MADSEN 'DEFAULT'
START POINT
XV MADSEN X1 3.0
XV MADSEN X2 1.0
XV MADSEN U 1.0
ELEMENT TYPE
EV SQ X
EV 2PR X Y
EV SIN X
EV COS X
ELEMENT USES
T X1SQ SQ
ZV X1SQ X X1
T X2SQ SQ
ZV X2SQ X X2
T X1X2 2PR
ZV X1X2 X X1
ZV X1X2 Y X2
T SX1 SIN
ZV SX1 X X1
T CX2 COS
ZV CX2 X X2
GROUP USES
E C1 X1SQ -1.0 X2SQ -1.0
E C1 X1X2 -1.0
E C2 X1SQ 1.0 X2SQ 1.0
E C2 X1X2 1.0
E C3 SX1 -1.0
E C4 SX1 1.0
E C5 CX2 -1.0
E C6 CX2 1.0
OBJECT BOUND
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS MADSEN
TEMPORARIES
R S
R C
M SIN
M COS
INDIVIDUALS
T SQ
F X * X
G X X + X
H X X 2.0
T 2PR
F X * Y
G X Y
G Y X
H X Y 1.0
T SIN
A S SIN( X )
A C COS( X )
F S
G X C
H X X - S
T COS
A S SIN( X )
A C COS( X )
F C
G X - S
H X X - C
ENDATA