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POWELLBS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME POWELLBS
* Problem :
* *********
* Powell badly scaled problem.
* This problem is a sum of n-1 sets of 2 groups, both involving
* nonlinear elements and being of the least square type.
* It Hessian matrix is tridiagonal.
* Source: Problem 3 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 Toint#34, Buckley#22 (p. 82).
* SIF input: Ph. Toint, Dec 1989.
* classification NOR2-AN-2-2
* N is the number of free variables
IE N 2
* Define useful parameters
IE 1 1
IE 2 2
IA N-1 N -1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N-1
XE A(I)
XE B(I)
ND
CONSTANTS
DO I 1 N-1
X POWELLBS A(I) 1.0
X POWELLBS B(I) 1.0001
ND
BOUNDS
FR POWELLBS 'DEFAULT'
START POINT
* Starting point for the 2 variables problem
X POWELLBS X(1) 0.0
X POWELLBS X(2) 1.0
ELEMENT TYPE
EV PROD V1 V2
EV EXPN V1
ELEMENT USES
DO I 1 N-1
IA I+1 I 1
XT AE(I) PROD
ZV AE(I) V1 X(I)
ZV AE(I) V2 X(I+1)
XT BE1(I) EXPN
ZV BE1(I) V1 X(I)
XT BE2(I) EXPN
ZV BE2(I) V1 X(I+1)
ND
GROUP USES
DO I 1 N-1
XE A(I) AE(I)
XE B(I) BE1(I) BE2(I)
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS POWELLBS
TEMPORARIES
R BIG
R BIGV1
R EXPMV
M EXP
INDIVIDUALS
* Product type elements
T PROD
A BIG 10000.0
A BIGV1 BIG * V1
F BIGV1 * V2
G V1 BIG * V2
G V2 BIGV1
H V1 V1 0.0
H V1 V2 BIG
H V2 V2 0.0
* Negative exponential type elements
T EXPN
A EXPMV EXP( - V1 )
F EXPMV
G V1 - EXPMV
H V1 V1 EXPMV
ENDATA