  The purpose of this paper is to present a boosted scaled subgradient-type
method (BSSM) to minimize the difference of two convex functions (DC
functions), where the first function is differentiable and the second one is
possibly non-smooth. Although the objective function is in general non-smooth,
under mild assumptions, the structure of the problem allows to prove that the
negative scaled generalized subgradient at the current iterate is a descent
direction from an auxiliary point. Therefore, instead of applying the Armijo
linear search and computing the next iterate from the current iterate, both the
linear search and the new iterate are computed from that auxiliary point along
the direction of the negative scaled generalized subgradient. As a consequence,
it is shown that the proposed method has similar asymptotic convergence
properties and iteration-complexity bounds as the usual descent methods to
minimize differentiable convex functions employing Armijo linear search.
Finally, for a suitable scale matrix the quadratic subproblems of BSSM have a
closed formula, and hence, the method has a better computational performance
than classical DC algorithms which must solve a convex (not necessarily
quadratic) subproblem.
