If the function you're minimizing is continuous, there is no point in imposing such a constraint. If the unconstrained minimum does not occur at b=d, then the constraint will get enforced automatically by solving the unconstrained problem.
If the unconstrained minimum does occur at b=d, then the constrained minimum is undefined. The function can always be made arbitrarily smaller by letting
b-d-->0
asymptotically. Any algorithm applied to such a problem would have to converge to the minimizing point satisfying b=d even if each iteration of the algorithm satisfied b~=d. it It would be like trying to minimize
f(x) = x^2 s.t. x>0
