The work is divided in two parts. The first part is concerned with the relationship between the d.c. optimization problem. In this sence we geralize the TOLAND´s relation (1979): inf { g(x) - h(x) } = inf { h(asteristic)(y) - g (asteristic)(y) }, H H And the GABAY´s relation (1982): inf { g(x) - h(x) } = inf { g lambda (x) - h lambda (x) } H H Where g, h, are l.s.c. convex functions, g(asteristic) and h(asteristic) are their conjugates, H is a real Hilbert space, and g lambda, h lambda, are the inf-convolution of g and h respectively, with the núcleos 8( . ) = (2 lambda)- 1 l l . l l 2 , lambda > 0. In the second part we present a new algorithm for dealing with d.c. functions. It is a descent method of proximal kind which takes in consideration the convex properties of the two convex functions separately