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October 12, 2025Open Access

A new insight into Lagrange duality on DC optimization

Key Points

Strong duality conditions are established for the new Lagrange dual problem in DC optimization, enhancing theoretical understanding.
The study critiques standard methods, highlighting how a more general class of functions influences duality relationships.
Weak duality is not inherently guaranteed in DC optimization, necessitating specific conditions to achieve it.
Explores a new dual formulation under the additivity condition, indicating potential advancements in optimization techniques.

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).

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