The Computation of Stationary Points on General Polytopes

Abstract

In this chapter we introduce an algorithm to solve the nonlinear stationary point problem on general polytopes in ℝ ⁿ. Recall that given an arbitrary polytope P and a function f: P ↦ ℝⁿ the problem of stationary point (or variational inequality) for f on P is to find a point x* ∈ P such that

$${({x^*} - x)^T}f({x^*}) \geqslant 0$$

, for all x ∈ P .