PENTDI.SIF

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* SET UP THE INITIAL DATA *
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NAME          PENTDI

*   Problem:
*   ********

*   A convex quadratic 5-diagonals problem in non-negative variables,
*   whose matrix has been taken from a paper of Pang and Liu.  
*   The interesting feature of this matrix is that its condition number 
*   increases with its order.  

*   Source:
*   a contribution to fullfill the LANCELOT academic licence agreement,
*   inspired by
*   Y. Lin and J. Pang,
*   "Iterative methods for large convex quadratic programs: a survey",
*   SIAM Journal on Control and Optimization 25, pp.383-411, 1987.

*   SIF input: J. Judice, University of Coimbra, January 1995.
*              condensed by Ph. Toint, January 1995.

*   classification QBR2-AN-V-0

*   dimension of the problem (should be even)

*IE N                   50             $-PARAMETER
*IE N                   100            $-PARAMETER
*IE N                   500            $-PARAMETER
*IE N                   1000           $-PARAMETER  original value
 IE N                   5000           $-PARAMETER

*   constants

 IE 1                   1  
 IE 2                   2
 IA N+1       N         1
 IA N-2       N         -2
 I/ N/2       N                        2
 IA N/2-1     N/2       -1
 IA N/2+1     N/2       1
 IA N/2+3     N/2       3

VARIABLES

 DO I         1                        N
 X  X(I)
 OD I

GROUPS

 XN OBJ
 XN OBJ0
 XN OBJ1      X(1)      -3.000         X(2)       1.000    
 XN OBJ1      X(N/2-1)   1.000         X(N/2)    -3.000    
 XN OBJ1      X(N/2+1)   4.000  
  
 DO I         N/2+3                    N
 XN OBJ1      X(I)       1.000    
 OD I

ELEMENT TYPE

 EV SQ        V
 EV 2PR       X                        Y

ELEMENT USES

 DO I         1                        N
 XT Z(I)      SQ
 ZV Z(I)      V                        X(I)
 OD I

 I= P         N
 DO I         1                        N-2
 IA I+1       I            1
 IA I+2       I            2
 IA P         P            1
 XT Z(P)      2PR
 ZV Z(P)      X                        X(I)
 ZV Z(P)      Y                        X(I+1)
 IA P         P            1
 XT Z(P)      2PR
 ZV Z(P)      X                        X(I)
 ZV Z(P)      Y                        X(I+2)
 OD I

GROUP USES

 DO I         1                        N
 XE OBJ0      Z(I)         6.000    
 OD I

 DO I         N+1                      P
 DI I         2
 IA I+1       I            1
 XE OBJ       Z(I)         -4.000    
 XE OBJ       Z(I+1)       1.000 
 OD I

OBJECT BOUND

*LO SOLUTION               -0.75

ENDATA

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

INDIVIDUALS

 T  2PR
 F                      X*Y
 G  X                   Y
 G  Y                   X
 H  X         Y         1.0

 T  SQ
 F                      V*V
 G  V                   V+V
 H  V         V         2.0

ENDATA