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BT6.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME BT6
* Problem :
* *********
* Source: problem 6 in
* P.T. Boggs and J.W. Tolle,
* "A strategy for global convergence in a sequential
* quadratic programming algorithm",
* SINUM 26(3), pp. 600-623, 1989.
* The problem is not convex.
* SIF input: Ph. Toint, June 1993.
* classification OOR2-AY-5-2
VARIABLES
X1
X2
X3
X4
X5
GROUPS
N OBJ
E CON1
E CON2 X2 1.0
CONSTANTS
RF ROOT2 SQRT 2.0
R+ 2ROOT2 ROOT2 ROOT2
RA 8+ROOT2 ROOT2 8.0
Z BT6 CON1 2ROOT2
Z BT6 CON2 8+ROOT2
BOUNDS
FR BT6 'DEFAULT'
START POINT
* Start 1
XV BT6 'DEFAULT' 2.0
* Start 2
*XV BT6 'DEFAULT' 8.0
* Solution proposed in the paper (infeasible)
*XV BT6 X1 1.1662
*XV BT6 X2 1.1821
*XV BT6 X3 1.3803
*XV BT6 X4 1.5060
*XV BT6 X5 0.61092
ELEMENT TYPE
EV SSQ X
EP SSQ P
EV ISQ X Y
IV ISQ Z
EV XY2 X Y
EV ISIN X Y
IV ISIN Z
EV X4Y2 X Y
ELEMENT USES
T O1 SSQ
V O1 X X1
P O1 P 2.0
T O2 ISQ
V O2 X X1
V O2 Y X2
T O3 SSQ
V O3 X X3
P O3 P 2.0
T O4 SSQ
V O4 X X4
P O4 P 4.0
T O5 SSQ
V O5 X X5
P O5 P 6.0
T C1E1 XY2
V C1E1 X X4
V C1E1 Y X1
T C1E2 ISIN
V C1E2 X X4
V C1E2 Y X5
T C2E1 X4Y2
V C2E1 X X3
V C2E1 Y X2
GROUP USES
E OBJ O1 O2
E OBJ O3 O4
E OBJ O5
E CON1 C1E1 C1E2
E CON2 C2E1
OBJECT BOUND
* Solution
*LO SOLTN 0.277044924
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS BT6
TEMPORARIES
R T
R SZ
M SIN
M COS
INDIVIDUALS
T SSQ
A T X - 1.0
F T ** P
G X P * T ** ( P - 1.0 )
H X X P * ( P - 1.0 ) * T ** ( P - 2.0 )
T ISQ
R Z X 1.0 Y -1.0
F Z * Z
G Z Z + Z
H Z Z 2.0
T ISIN
R Z X 1.0 Y -1.0
A SZ SIN( Z )
F SZ
G Z COS( Z )
H Z Z -SZ
T XY2
F X * Y * Y
G X Y * Y
G Y 2.0 * X * Y
H X Y Y + Y
H Y Y X + X
T X4Y2
F X**4 * Y**2
G X 4.0 * X**3 * Y**2
G Y 2.0 * X**4 * Y
H X X 12.0 * X**2 * Y**2
H X Y 8.0 * X**3 * Y
H Y Y 2.0 * X**4
ENDATA