A Shadow Simplex Method for Infinite Linear Programs

We present a simplex-type algorithm—that is, an algorithm that moves from one extreme point of the infinite-dimensional feasible region to another, not necessarily adjacent, extreme point—for solving a class of linear programs with countably infinite variables and constraints. Each iteration of this method can be implemented in finite time, whereas the solution values converge to the optimal value as the number of iterations increases. This simplex-type algorithm moves to an adjacent extreme point and hence reduces to a true infinite-dimensional simplex method for the important special cases of nonstationary infinite-horizon deterministic and stochastic dynamic programs.