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A path-following algorithm is proposed for finding a solution to the nonlinear stationary point problem on an unbounded, convex, and pointed polyhedron. The algorithm can start at an arbitrary point of the polyhedron. The path to be followed by the algorithm is described as the path of zeros of some piecewise continuously differentiable function defined on an appropriate subdivided manifold. This manifold is induced by a generalized primal-dual pair of subdivided manifolds. The path of zeros can be approximately followed by dividing the polyhedron into simplices and replacing the original function by its piecewise linear approximation with respect to this subdivision. The piecewise linear path of this function can be generated by alternating replacement steps and linear programming pivot steps. A condition under which the path of zeros converges to a solution is also stated, and a description of how the algorithm operates when the problem is linear or when the polyhedron is the Cartesian product of a poly...

A Simplicial Algorithm for the Nonlinear Stationary Point Problem on an Unbounded Polyhedron