new problem BOXPOWER added

git-svn-id: http://ccpforge.cse.rl.ac.uk/svn/cutest/sif/trunk@157 ca3beb79-f7c6-489d-80df-314e45fd556d

BOXPOWER.SIF

@@ -0,0 +1,109 @@
+***************************
+* 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