Mangasarian-type second- and higher-order duality for mathematical programs with complementarity constraints

Based on the strong stationary condition, we formulate second-order and higher order duals for a mathematical program with complementary constraints (MPCC). Under suitable generalized convexity assumptions, we then propose several duality theorems for second and higher order duality in MPCC problems, including the weak duality, strong duality, converse duality, and strict converse duality theorems. Moreover, we present examples to illustrate these results, where one of them reveals that a lower bound provided by our proposed second-order duality is tighter than the one given by the first-order duality.