HUBFIT.SIF

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* SET UP THE INITIAL DATA *
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NAME          HUBFIT

*   Problem :
*   *********
*   Variable dimension full rank linear problem
*   An elementary fit using the Huber loss function

*   Source:
*   A.R. Conn, N. Gould and Ph.L. Toint,
*   "The LANCELOT User's Manual",
*   Dept of Maths, FUNDP, 1991.

*   SIF input: Ph. Toint, Jan 1991.

*   classification OLR2-AN-2-1

*   Data points
 RE X1                  0.1
 RE X2                  0.3
 RE X3                  0.5
 RE X4                  0.7
 RE X5                  0.9
*   Observed values
 RE Y1                  0.25
 RE Y2                  0.3
 RE Y3                  0.625
 RE Y4                  0.701
 RE Y5                  1.0
*   Upper bound at 1.0
 RE C                   0.85
VARIABLES
    a
    b
GROUPS
*   Objective function groups
 ZN Obj1      a                        X1
 XN Obj1      b         1.0
 XN Obj1      'SCALE'   2.0
 ZN Obj2      a                        X2
 XN Obj2      b         1.0
 XN Obj2      'SCALE'   2.0
 ZN Obj3      a                        X3
 XN Obj3      b         1.0
 XN Obj3      'SCALE'   2.0
 ZN Obj4      a                        X4
 XN Obj4      b         1.0
 XN Obj4      'SCALE'   2.0
 ZN Obj5      a                        X5
 XN Obj5      b         1.0
 XN Obj5      'SCALE'   2.0
*   Constraint group
 XL Cons      a         1.0            b         1.0
CONSTANTS
 Z  HUBFIT    Obj1                     Y1
 Z  HUBFIT    Obj2                     Y2
 Z  HUBFIT    Obj3                     Y3
 Z  HUBFIT    Obj4                     Y4
 Z  HUBFIT    Obj5                     Y5
 Z  HUBFIT    Cons                     C
BOUNDS
 XR HUBFIT    b
GROUP TYPE
 GV HUBER     ALPHA
GROUP USES
 XT Obj1      HUBER
 XT Obj2      HUBER
 XT Obj3      HUBER
 XT Obj4      HUBER
 XT Obj5      HUBER
ENDATA

GROUPS        HUBFIT
TEMPORARIES
 L  OUT
 L  NEGOUT
 L  POSOUT
 R  ABSA
 R  HUBERK
 R  FF
 R  GG
 R  HH
 M  ABS
INDIVIDUALS
 T  HUBER
 A  HUBERK              1.5
 A  ABSA                ABS( ALPHA )
 A  OUT                 ABSA .GT. HUBERK
*  Case 1: alpha is outside [-k, k]
 I  OUT       FF        HUBERK * ABSA - 0.5 * HUBERK * HUBERK
 A  NEGOUT              OUT .AND. ( ALPHA .LT. 0.0 )
 A  POSOUT              OUT .AND. ( ALPHA .GE. 0.0 )
 I  POSOUT    GG        HUBERK
 I  NEGOUT    GG        - HUBERK
 I  OUT       HH        0.0
*  Case 2: alpha is inside [-k, k]
 E  OUT       FF        0.5 * ABSA * ABSA
 E  OUT       GG        ALPHA
 E  OUT       HH        1.0
*  Assign the final values
 F                      FF
 G                      GG
 H                      HH
ENDATA