A d.c. set is a set which is the difference of two convex sets. The paper shows that any set can be viewed as the image of a d.c. set under an appropriate linear mapping. Using this universality it can convert any problem of finding an element of a given compact set in ℝn into one of finding an element of a d.c. set. On the basis of this approach a method is developed for solving a system of nonlinear equations-inequations. Unlike Newton-type methods, the present method does not require either convexity, differentiability assumptions or an initial approximate solution.
