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POWELLSG.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME POWELLSG
* Problem :
* *********
* The extended Powell singular problem.
* This problem is a sum of n/4 sets of four terms, each of which is
* assigned its own group.
* Source: Problem 13 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#19, Buckley#34 (p.85)
* SIF input: Ph. Toint, Dec 1989.
* classification OUR2-AN-V-0
* N is the number of free variables, and should be a multiple of 4
*IE N 4 $-PARAMETER original value
*IE N 8 $-PARAMETER
*IE N 16 $-PARAMETER
*IE N 20 $-PARAMETER
*IE N 36 $-PARAMETER
*IE N 40 $-PARAMETER
*IE N 60 $-PARAMETER
*IE N 80 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 500 $-PARAMETER
*IE N 1000 $-PARAMETER
IE N 5000 $-PARAMETER
*IE N 10000 $-PARAMETER
* Define useful parameters
IE 1 1
IE 4 4
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N
DI I 4
IA I+1 I 1
IA I+2 I 2
IA I+3 I 3
XN G(I) X(I) 1.0 X(I+1) 10.0
XN G(I+1) X(I+2) 1.0 X(I+3) -1.0
XN G(I+1) 'SCALE' 0.2
XN G(I+2) X(I+1) 1.0 X(I+2) -2.0
XN G(I+3) X(I) 1.0 X(I+3) -1.0
XN G(I+3) 'SCALE' 0.1
ND
BOUNDS
FR POWELLSG 'DEFAULT'
START POINT
DO I 1 N
DI I 4
IA I+1 I 1
IA I+2 I 2
IA I+3 I 3
X POWELLSG X(I) 3.0
X POWELLSG X(I+1) -1.0
X POWELLSG X(I+2) 0.0
X POWELLSG X(I+3) 1.0
ND
GROUP TYPE
GV L2 GVAR
GV L4 GVAR
GROUP USES
DO I 1 N
DI I 4
IA I+1 I 1
IA I+2 I 2
IA I+3 I 3
XT G(I) L2
XT G(I+1) L2
XT G(I+2) L4
XT G(I+3) L4
ND
OBJECT BOUND
LO POWELLSG 0.0
* Solution
*LO SOLTN 0.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS POWELLSG
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