Mathematical Programming

, Volume 58, Issue 1–3, pp 415–428

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

• Phan Thien Thach
Article

## Abstract

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 ℝ 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.

## Key words

D.c. sets d.c. functions nonlinear equations—inequations

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