A homotopy continuation method for solving normal equations

In this paper, we present a continuation method for solving normal equations generated byC² functions and polyhedral convex sets. We embed the normal map into a homotopyH, and study the existence and characteristics of curves inH¹(0) starting at a specificd point. We prove the convergence of such curves to a solution of the normal equation under some conditions on the polyhedral convex setC and the functionf. We prove that the curve will have finite are length if the normal map, associated with the derivative df(·) and the critical coneK, is coherently oriented at each zero of the normal mapf_c inside a certain ball of ⁿ. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.This research was performed at the Department of Industrial Engineering, University of Wisconsin-Madison, Madison, WI, USA.