D.c. sets,d.c. functions and nonlinear equations

Ad.c. set is a set which is the difference of two convex sets. We show that any set can be viewed as the image of a d.c. set under an appropriate linear mapping. Using this universality we can convert any problem of finding an element of a given compact set in ⁿ 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, our method does not require either convexity, differentiability assumptions or an initial approximate solution.The revision of this paper was produced during the author's stay supported by a Sophia lecturing-research grant at Sophia University (Tokyo, Japan).