A new insight into Lagrange duality on DC optimization

Abstract

In this paper we present a new Lagrange dual problem associated to a primal DC optimization problem under the additivity condition (AC). As usual for DC programming, even weak duality is not guaranteed for free and, due to this issue, we investigate conditions not only for weak, but also for strong duality between this dual and the primal DC problem. In addition, we also analyze conditions for strong duality between the primal and its standard Lagrange dual problem utilizing a revisited regularity condition which is guaranteed by a more general class of functions than the one used in a prior work (see [14]).