Dear Members of the community
I am trrying to solve complementarity problems w=Mz+q
with complentarity variables w and z. A way to solve the problem is to transform the original one to a set of inequaities. For instance, for M{{2,1},{1,2}} and q={-5,-6} the set of inequalities to be sol is
{2 z1 + z2 + 10 d1 <= 15, z1 + 2 z2 + 10 d2 <= 16, z1 - 10 d1 <= 0,
z2 - 10 d2 <= 0, -2 z1 - z2 <= -5, -z1 - 2 z2 <= -6, -z1 <= 0, -z2 <=
0}
I have tried to solve with Solve[] like this
Solve[{2 z1 + z2 + 10 d1 <= 15, z1 + 2 z2 + 10 d2 <= 16,
z1 - 10 d1 <= 0,
z2 - 10 d2 <= 0, -2 z1 - z2 <= -5, -z1 - 2 z2 <= -6, -z1 <=
0, -z2 <= 0}, {z1, z2, d1, d2}, {Element[{z1, z2}, Reals],
Element[d1, {0, 1}], Element[d2, {0, 1}]}]
getting an error: Solve::ivar: d1[Element]{0,1} is not a valid variable. Can Mathematica solve this type of inequalities?
I´ll appreciate any help given.
Jesus