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EDENSCH.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME EDENSCH
* Problem :
* *********
* The extended Dennis and Schnabel problem, as defined by Li.
* Source:
* G. Li,
* "The secant/finite difference algorithm for solving sparse
* nonlinear systems of equations",
* SIAM Journal on Optimization, (to appear), 1990.
* SIF input: Ph. Toint, Apr 1990.
* minor correction by Ph. Shott, January 1995.
* classification OUR2-AN-V-0
* Number of variables (at least 2)
*IE N 36 $-PARAMETER original value
IE N 2000 $-PARAMETER
* Constants
IE 1 1
* Computed parameters
IA N-1 N -1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N-1
IA I+1 I 1
XN A(I) X(I) 1.0
XN B(I) X(I+1) -2.0
XN C(I) X(I+1) 1.0
ND
XN A(N) X(N) 0.0
CONSTANTS
DO I 1 N-1
X EDENSCH A(I) 2.0
X EDENSCH C(I) -1.0
ND
X EDENSCH A(N) 2.0
BOUNDS
FR EDENSCH 'DEFAULT'
START POINT
XV EDENSCH 'DEFAULT' 8.0
ELEMENT TYPE
EV 2PR X Y
ELEMENT USES
XT 'DEFAULT' 2PR
DO I 1 N-1
IA I+1 I 1
ZV E(I) X X(I)
ZV E(I) Y X(I+1)
ND
GROUP TYPE
GV L2 GVAR
GV L4 GVAR
GROUP USES
XT 'DEFAULT' L2
DO I 1 N-1
XT A(I) L4
XE B(I) E(I)
ND
XT A(N) L4
OBJECT BOUND
LO EDENSCH 0.0
* Solution
*LO SOLTN(36) 219.28
*LO SOLTN(2000) 1.20032D+04
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS EDENSCH
INDIVIDUALS
T 2PR
F X * Y
G X Y
G Y X
H X Y 1.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS EDENSCH
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
T L4
F GVAR**4
G 4.0 * GVAR**3
H 12.0 * GVAR**2
ENDATA