In this paper, we present a continuation method for solving normal equations generated by C2 functions and polyhedral convex sets. We embed the normal map into a homotopy H, and study the existence and characteristics of curves in H–1(0) starting at a specified point. We prove the convergence of such curves to a solution of the normal equation under some conditions on the polyhedral convex set C and the function f. We prove that the curve will have finite arc length if the normal map, associated with the derivative df(·) and the critical cone K, is coherently oriented at each zero of the normal map fc inside a certain ball of ℝn.
