Quotient gradient methods for solving constraint satisfaction problems

In this paper, we propose a novel systematic method for locating multiple disjoint feasible regions for a general constraint satisfaction problems (or non-linearly constrained systems of equations). A theoretical foundation of the novel method is developed on the basis of the stability theory for a class of non-hyperbolic dynamical systems. The proposed method consists of the following: (i) approach a feasible region and (ii) escape from a feasible region and move toward another feasible region. Two numerical examples are given to illustrate the proposed method