NOTES ON LOWER-LEVEL DUALITY APPROACH FOR BILEVEL PROGRAMS

This paper focuses on a new approach based on lower-level Wolfe and Mond-Weir duality for bilevel programs, which gives two new single-level reformulations called WDP and MDP, respectively. Different from the popular MPCC (i.e., mathematical program with complementarity constraints) approach, both WDP and MDP may satisfy the Mangasarian-Fromovitz constraint qualification at their feasible points. This paper aims at exploring whether these new reformulations satisfy other constraint qualifications such as Abadie CQ and Guignard CQ. In particular, some sufficient conditions to ensure Abadie CQ and Guignard CQ to hold for WDP and MDP are derived.