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GENROSE.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME GENROSE
* Problem :
* --------
* The generalized Rosenbrock function.
* Source: problem 5 in
* S. Nash,
* "Newton-type minimization via the Lanczos process",
* SIAM J. Num. Anal. 21, 1984, 770-788.
* SIF input: Nick Gould, Oct 1992.
* minor correction by Ph. Shott, Jan 1995.
* classification SUR2-AN-V-0
* Number of variables
*IE N 5 $-PARAMETER
*IE N 10 $-PARAMETER
*IE N 100 $-PARAMETER
IE N 500 $-PARAMETER
* other parameter definitions
IE 1 1
IE 2 2
IA N-1 N -1
IA N+1 N 1
RI RN+1 N+1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
N OBJ
DO I 2 N
XN Q(I) 'SCALE' 0.01
XN Q(I) X(I) 1.0
XN L(I) X(I) 1.0
ND
CONSTANTS
GENROSE OBJ -1.0
DO I 2 N
X GENROSE L(I) 1.0
ND
BOUNDS
FR GENROSE 'DEFAULT'
START POINT
* start with X(I) = I/N+1.
DO I 1 N
RI RI I
R/ T RI RN+1
ZV GENROSE X(I) T
ND
ELEMENT TYPE
EV MSQR V
ELEMENT USES
XT 'DEFAULT' MSQR
DO I 2 N
IA I-1 I -1
ZV Q(I) V X(I-1)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
XT 'DEFAULT' L2
DO I 2 N
XE Q(I) Q(I)
ND
OBJECT BOUND
LO GENROSE 1.0
* Solution
*LO SOLTN 1.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS GENROSE
INDIVIDUALS
T MSQR
F - V ** 2
G V - 2.0D+0 * V
H V V - 2.0D+0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS GENROSE
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA