Lagrange duality in canonical DC programming

• Lagrange-type duality for a canonical DC programming problem is given.
• Constraint qualifications (CQ1) and (CQ2) are given.
• Weak duality always holds, and strong duality holds under (CQ1) or (CQ2).
• (CQ1), (CQ2), and previous ones in [7] in this setting are compared.

We study Lagrange duality theorems for canonical DC programming problems. We show two types Lagrange duality results by using a decomposition method to infinite convex programming problems and by using a previous result by Lemaire (1998)  [6]. Also we observe these constraint qualifications for the duality theorems.