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BROWNBS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME BROWNBS
* Problem :
* *********
* Brown badly scaled problem in 2 variables.
* This problem is a sum of n-1 sets of 3 groups, one of then involving
* a nonlinear element and all being of the least square type.
* It Hessian matrix is tridiagonal.
* Source: Problem 4 in
* J.J. More', B.S. Garbow and K.E. Hillstrom,
* "Testing Unconstrained Optimization Software",
* ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
* See also Buckley#25
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-AN-2-0
* N is the number of free variables
IE N 2
* Define useful parameters
IE 1 1
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) 1.0
XN C(I)
ND
CONSTANTS
DO I 1 N-1
X BROWNBS A(I) 1000000.0
X BROWNBS B(I) 0.000002
X BROWNBS C(I) 2.0
ND
BOUNDS
FR BROWNBS 'DEFAULT'
START POINT
XV BROWNBS 'DEFAULT' 1.0
ELEMENT TYPE
EV 2PR V1 V2
ELEMENT USES
XT 'DEFAULT' 2PR
DO I 1 N-1
IA I+1 I 1
ZV CE(I) V1 X(I)
ZV CE(I) V2 X(I+1)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
XT 'DEFAULT' L2
DO I 1 N-1
XE C(I) CE(I)
ND
OBJECT BOUND
LO BROWNBS 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS BROWNBS
INDIVIDUALS
T 2PR
F V1 * V2
G V1 V2
G V2 V1
H V1 V2 1.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS BROWNBS
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA