unified duality for mathematical programming problems with vanishing constraints

In this article, we formulate a new mixed-type dual problem for a mathematical program with vanishing constraints. the presented dual problem does not involve the index set, however, the dual models contain the calculations of index sets, which makes it difficult to solve these models from an algorithm point of view. the weak, strong and strict converse duality theorems are discussed in order to establish the relationships between the mathematical program with vanishing constraints and its mixed type dual under generalized convexity. to validate the results, a non-trivial example is discussed. our dual model unifies the dual models discussed in [q. hu, j. wang, y. chen, new dualities for mathematical programs with vanishing constraints, annals of operations research, 287 (2020) 233-255].