  We present a version of GMI (Gomory mixed-integer) cuts in a way so that they
are derived with respect to a "dual form" mixed-integer optimization problem
and applied on the standard-form primal side as columns, using the primal
simplex algorithm. This follows the general scheme of He and Lee, who did the
case of Gomory pure-integer cuts.
  Our input mixed-integer problem is not in standard form, and so our cuts are
derived rather differently from how they are normally derived. A convenient way
to develop GMI cuts is from MIR (mixed-integer rounding) cuts, which are
developed from 2-dimensional BMI (basic mixed integer) cuts, which involve a
nonnegative continuous variable and an integer variable. The nonnegativity of
the continuous variable is not the right tool for us, as our starting point
(the "dual form" mixed-integer optimization problem) has no nonnegativity. So
we work out a different 2-dimensional starting point, a pair of somewhat
arbitrary inequalities in one continuous and one integer variable. In the end,
we follow the approach of He and Lee, getting now a finitely converging
primal-simplex column-generation algorithm for mixed-integer optimization
problems.
