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BOXPOWER.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME BOXPOWER
* Problem :
* *********
* Source:
*
* function with a "box-shapped" singular Hessian
* SIF input: Nick Gould, June 2013
* classification OUR2-AN-V-0
* Number of variables
*IE N 10 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 1000 $-PARAMETER
IE N 10000 $-PARAMETER original value
IE N 20000 $-PARAMETER
*IE N 10 $-PARAMETER
* Singularity type p leading to term x^2(p+1)
IE P 9
* Other parameters
IE 1 1
IE 2 2
IA N-1 N -1
IA P+1 P 1
IM 2P+2 P+1 2
RI POWER 2P+2
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
XN G(1) X(1) 1.0
DO I 2 N-1
XN G(I) X(1) 1.0 X(I) 1.0
XN G(I) X(N) 1.0
ND
XN G(N) X(N) 1.0
BOUNDS
FR BOXPOWER 'DEFAULT'
START POINT
XV BOXPOWER 'DEFAULT' 0.99
GROUP TYPE
GV L2 GVAR
GV POWER GVAR
GP POWER P
GROUP USES
DO I 1 N-1
XT G(I) L2
ND
XT G(N) POWER
ZP G(N) P POWER
OBJECT BOUND
* Least square problems are bounded below by zero
LO POWER 0.0
* Solution
*LO SOLTN 0.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS BOXPOWER
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
T POWER
F GVAR ** P
G P * GVAR ** ( P - 1.0 )
H P * ( P - 1.0 ) * GVAR ** ( P - 2.0 )
ENDATA