LSQFIT.SIF

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* SET UP THE INITIAL DATA *
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NAME          LSQFIT

*   Problem :
*   *********
*   An elementary constrained linear least-squares fit

*   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 SLR2-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  LSQFIT    Obj1                     Y1
 Z  LSQFIT    Obj2                     Y2
 Z  LSQFIT    Obj3                     Y3
 Z  LSQFIT    Obj4                     Y4
 Z  LSQFIT    Obj5                     Y5
 Z  LSQFIT    Cons                     C
BOUNDS
 XR LSQFIT    b
GROUP TYPE
 GV SQUARE    ALPHA
GROUP USES
 XT Obj1      SQUARE
 XT Obj2      SQUARE
 XT Obj3      SQUARE
 XT Obj4      SQUARE
 XT Obj5      SQUARE
ENDATA

GROUPS        LSQFIT
INDIVIDUALS
 T  SQUARE
 F                      ALPHA * ALPHA
 G                      ALPHA + ALPHA
 H                      2.0
ENDATA