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.

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