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QRTQUAD.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME QRTQUAD
* Problem :
* *********
* An unconstrained problem involving elements with different degree of
* nonlinearity (quartics and quadratics). It contains N elements the first
* M of which are quartic. The Hessian is tridiagonal for the first M
* elements and arrow-head for the remaining ones. The first M variables
* have lower and upper bounds.
* SIF input: Ph. Toint, June 1992.
* minor correction by Ph. Shott, Jan 1995.
* classification OBR2-MN-V-0
*IE N 12 $-PARAMETER
*IE N 120 $-PARAMETER original value
*IE N 1200 $-PARAMETER
IE N 5000 $-PARAMETER
*IE M 6 $-PARAMETER
*IE M 10 $-PARAMETER original value
*IE M 100 $-PARAMETER
IE M 1100 $-PARAMETER
* Define constants
IE 0 0
IE 1 1
IE 2 2
IA M+1 M 1
IA N-1 N -1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N
RI RI I
RM C RI - 10.0
ZN OBJ X(I) C
ND
CONSTANTS
BOUNDS
XR QRTQUAD 'DEFAULT'
DO I 1 M
XL QRTQUAD X(I) 0.0
XU QRTQUAD X(I) 10.0
OD I
START POINT
ELEMENT TYPE
EV QUART X Y
EP QUART P
EV QUAD X Y
ELEMENT USES
XT 'DEFAULT' QUAD
RI RM M
DO I 1 M
RI RI I
R/ C RI RM
I+ I+1 I 1
XT E(I) QUART
ZV E(I) X X(I)
ZV E(I) Y X(I+1)
ZP E(I) P C
OD I
DO I M+1 N-1
ZV E(I) X X(I)
ZV E(I) Y X(N)
OD I
GROUP USES
DO I 1 N-1
XE OBJ E(I)
OD I
OBJECT BOUND
LO QRTQUAD 0.0
* Solution
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS QRTQUAD
TEMPORARIES
R XY
INDIVIDUALS
* Exponential of the product of X and Y divided by 10
T QUART
A XY X*Y
F P*XY**4
G X P*Y*4.0*XY**3
G Y P*X*4.0*XY**3
H X X 12.0*P*(Y**2)*(XY**2)
H Y Y 12.0*P*(X**2)*(XY**2)
H X Y 4.0*P*(XY**3) + 12.0*P*Y*X*(XY**2)
T QUAD
F 4.0 * X * X + 2.0 * Y * Y + X * Y
G X 8.0 * X + Y
G Y 4.0 * Y + X
H X X 8.0
H X Y 1.0
H Y Y 4.0
ENDATA