In this paper, we develop a version of the bundle method to solve
unconstrained difference of convex (DC) programming problems. It is
assumed that a DC representation of the objective function is available.
Our main idea is to utilize subgradients of both the first and second
components in the DC representation. This subgradient information is
gathered from some neighborhood of the current iteration point and it is
used to build separately an approximation for each component in the DC
representation. By combining these approximations we obtain a new
nonconvex cutting plane model of the original objective function, which
takes into account explicitly both the convex and the concave behavior
of the objective function. We design the proximal bundle method for DC
programming based on this new approach and prove the convergence of the
method to an ε-critical
point. The algorithm is tested using some academic test problems and
the preliminary numerical results have shown the good performance of the
new bundle method. An interesting fact is that the new algorithm finds
nearly always the global solution in our test problems.