$title Affine Variational Inequality (AFFINEVI,SEQ=48)

$onText
An affine VI is to find x in X:

F(x) (y - x) >= 0, for all y in X

Here F is an affine (linear) function and X is polyhedral:
e.g. X = { x >= 0 | Ax >= b }

This can be reformulated as an MCP:

0 <= F(x) - A'u   perpendicular to   x >= 0
0 <= Ax - b       perpendicular to   u >= 0

Contributor: Michael Ferris, February 2010
$offText

sets
 I  / i1 /
 J  / j1 * j2 /
 ;
alias(J,K);

table A(I,J)
       j1        j2
i1     -1        -1
;

parameter b(I) /
i1   -1
/;

table M(J,J)
       j1        j2
j1      1
j2      1         1
;

parameter q(J) /
j1  2
j2 -3
/;

positive variables
 x(J)  'primal vars, perp to f(J)'
 ;

equations
 F(J)
 g(I)
 ;

F(J)..      sum(K, M(J,K)* x(K)) + q(J)  =N= 0 ;
g(I)..      sum {j, A(I,J)*x(J)}         =g= b(I) ;

model affVI / F, g/;

file fx /"%emp.info%"/;
putclose fx 'vi F x g';

solve affVI using emp;