Linear Stationary Point Problems on Unbounded Polyhedra

In this paper we propose a complementary pivoting algorithm for finding a stationary point of an affine function on an unbounded polyhedron. Under some mild conditions there is a piecewise linear path from an arbitrarily chosen point in the polyhedron leading to a solution of the problem. By exploiting fully the linearity of the problem, each linear piece of the path is followed in principle by making just one linear programming pivoting step.