Lagrange-type duality in DC programming problems with equivalent DC inequalities

Abstract

Abstract In this paper, we provide Lagrange-type duality theorems for mathematical programming problems with DC objective and constraint functions. The class of problems to which Lagrange-type duality theorems can be applied is broader than the class in the previous research. The main idea is to consider equivalent inequality systems given by the maximization of the original functions. In order to compare the present results with the previously reported results, we describe the difference between their constraint qualifications, which are technical assumptions for the duality.

Keywords

• DC function
• DC programming problem
• Lagrange duality theorem
• constraint qualification