On the Solution of Nonlinear Equations by Path Methods.

摘要

The problem considered is that of finding a solution to a system of nonlinear equations subject to some auxiliary constraints. The methods studied here are called path methods, also referred to as continuation or global Newton methods, for solving equations. A general theory is developed which unifies the results from several papers and allows new methods to be analyzed easily. The new methods are shown to converge under more general boundary and monotonicity conditions than those assumed for the existing methods. A rigorous proof of convergence is given for an algorithm which implements a general path method. (Author)