$TITLE  DUALDISCR PROBLEM
$OFFUPPER
* This problem solves the dual of the infinite LP on pg 10 of
*  Anderson and Nash, by discretization.
*
*  References: 
*        The problem is taken from the book on Linear Programming
*        in Infinite Dimensional Spaces.
*
*  The number of discretization points is 11. The dimension
*   of I and the constant n need to be changed if the
*   number of discretization points are increase.

  SETS
       I   discretization points   / I1*I11 /
       J   discretization points   / J1*J11 /;

VARIABLES
  Y1(I)   
  Y2(I)   
  W1(J)   
  W2(J)   
  Z;

POSITIVE VARIABLES Y1, Y2, W1, W2 ;



SCALAR N number of discretization points /11/ ;

EQUATIONS
   COST   objective function
   CONSTR1  
   CONSTR2 ;

COST .. Z =E= SUM(I,2*Y1(I)+4*Y2(I))+SUM(J,W2(J));

CONSTR1 ..  
STRGL(J) .. SUM(I$(ORD(I) LE ORD(J)),(X1(I)-X2(I)))/N =G= 0;
* STRGL(J) .. SUM(I$(IND(I,J) NE 0),(X1(I)-X2(I)))/N =G= 0;

STRGU(J) .. SUM(I$(ORD(I) LE ORD(J)),(X1(I)-X2(I)))/N =L= 1;
*STRGU(J) .. SUM(I$IND(I,J),(X1(I)-X2(I)))/N =L= 1;

MODEL DISCRETIZE /ALL/;

SOLVE DISCRETIZE USING LP MAXIMIZING Z;

DISPLAY X1.L, X2.L, Z.L ;