CHNRSBNE.SIF

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* SET UP THE INITIAL DATA *
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NAME          CHNRSBNE

*   Problem :
*   --------
*   The chained Rosenbrock function (Toint),  nonlinear equation version.

*   Source:
*   Ph.L. Toint,
*   "Some numerical results using a sparse matrix updating formula in
*   unconstrained optimization",
*   Mathematics of Computation, vol. 32(114), pp. 839-852, 1978.

*   See also Buckley#46 (n = 25) (p. 45).
*   SIF input: Ph. Toint, Dec 1989.

*   classification NOR2-AN-V-V

*   Number of variables ( at most 50)

*IE N                   10             $-PARAMETER     original value
*IE N                   25             $-PARAMETER
 IE N                   50             $-PARAMETER

*   Problem data

 RE ALPH1               1.25
 RE ALPH2               1.40
 RE ALPH3               2.40
 RE ALPH4               1.40
 RE ALPH5               1.75
 RE ALPH6               1.20
 RE ALPH7               2.25
 RE ALPH8               1.20
 RE ALPH9               1.00
 RE ALPH10              1.10
 RE ALPH11              1.50
 RE ALPH12              1.60
 RE ALPH13              1.25
 RE ALPH14              1.25
 RE ALPH15              1.20
 RE ALPH16              1.20
 RE ALPH17              1.40
 RE ALPH18              0.50
 RE ALPH19              0.50
 RE ALPH20              1.25
 RE ALPH21              1.80
 RE ALPH22              0.75
 RE ALPH23              1.25
 RE ALPH24              1.40
 RE ALPH25              1.60
 RE ALPH26              2.00
 RE ALPH27              1.00
 RE ALPH28              1.60
 RE ALPH29              1.25
 RE ALPH30              2.75
 RE ALPH31              1.25
 RE ALPH32              1.25
 RE ALPH33              1.25
 RE ALPH34              3.00
 RE ALPH35              1.50
 RE ALPH36              2.00
 RE ALPH37              1.25
 RE ALPH38              1.40
 RE ALPH39              1.80
 RE ALPH40              1.50
 RE ALPH41              2.20
 RE ALPH42              1.40
 RE ALPH43              1.50
 RE ALPH44              1.25
 RE ALPH45              2.00
 RE ALPH46              1.50
 RE ALPH47              1.25
 RE ALPH48              1.40
 RE ALPH49              0.60
 RE ALPH50              1.50

*   other parameter definitions

 IE 1                   1
 IE 2                   2

VARIABLES

 DO I         1                        N
 X  X(I)
 ND

GROUPS

 DO I         2                        N
 IA I-1       I         -1
 XE SQ(I)     X(I-1)    1.0
 AM AI        ALPH(I)   1.0
 RM 4AI       AI        4.0
 RD SCL       4AI       1.0
 ZE SQ(I)     'SCALE'                  SCL
 XE B(I)      X(I)      1.0
 ND

CONSTANTS

 DO I         2                        N
 X  CHNRSBNE  B(I)      1.0
 ND

BOUNDS

 FR CHNRSBNE  'DEFAULT'

START POINT

 XV CHNROSMB  'DEFAULT' -1.0

ELEMENT TYPE

 EV ETYPE     V1
 EP ETYPE     GAMMA

ELEMENT USES

 XT 'DEFAULT' ETYPE

 DO I         2                        N
 ZV ELA(I)    V1                       X(I)
 XP ELA(I)    GAMMA      2.0
 ND

GROUP USES

 DO I         2                        N
 XE SQ(I)     ELA(I)
 ND

OBJECT BOUND

 LO CHNRSBNE            0.0

*   Solution

*LO SOLTN               0.0

ENDATA

***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES  *
***********************

ELEMENTS      CHNRSBNE

INDIVIDUALS

 T  ETYPE
 F                      - V1 ** GAMMA
 G  V1                  - GAMMA * V1 ** ( GAMMA - 1.0 )
 H  V1        V1        - GAMMA * ( GAMMA - 1.0 ) *
 H+                     V1 ** ( GAMMA - 2.0 )

ENDATA