ARGLALE.SIF

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* SET UP THE INITIAL DATA *
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NAME          ARGLALE

*   Problem :
*   *********
*   Variable dimension full rank linear problem, a linear equation version.

*   Source: Problem 32 in
*   J.J. More', B.S. Garbow and K.E. Hillstrom,
*   "Testing Unconstrained Optimization Software",
*   ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.

*   See also Buckley#80 (with different N and M)
*   SIF input: Ph. Toint, Dec 1989.

*   classification NLR2-AN-V-V

*   This is a(n infeasible) linear feasibility problem 

*   N is the number of free variables
*   M is the number of equations ( M.ge.N)

*IE N                   10             $-PARAMETER
*IE N                   50             $-PARAMETER 
*IE N                   100            $-PARAMETER
 IE N                   200            $-PARAMETER

*IE M                   20             $-PARAMETER .ge. N
*IE M                   100            $-PARAMETER .ge. N
*IE M                   200            $-PARAMETER .ge. N
 IE M                   400            $-PARAMETER .ge. N

*   Define useful parameters

 IE 1                   1
 RE -2.0                -2.0

 IA N+1       N         1
 RI RM        M
 R/ -2/M      -2.0                     RM
 RA 1-2/M     -2/M      1.0

VARIABLES

 DO I         1                        N
 X  X(I)
 ND

GROUPS

 DO I         1                        N
 IA I-1       I         -1
 IA I+1       I         1
 DO J         1                        I-1
 ZE G(I)      X(J)                     -2/M
 OD J
 ZE G(I)      X(I)                     1-2/M
 DO J         I+1                      N
 ZE G(I)      X(J)                     -2/M
 ND

 DO I         N+1                      M
 DO J         1                        N
 ZE G(I)      X(J)                     -2/M
 ND

CONSTANTS

 X  ARGLALE   'DEFAULT' 1.0

BOUNDS

 FR ARGLALE   'DEFAULT'

START POINT

 XV ARGLALE   'DEFAULT' 1.0

ENDATA