Optimality and Duality Results for Bilevel Programming Problem Using Convexifactors

The paper is devoted to the applications of convexifactors to bilevel programming problem. Here we have defined ∂∗-convex, ∂∗-pseudoconvex and ∂∗-quasiconvex bifunctions in terms of convexifactors on the lines of Dutta and Chandra (Optimization 53:77–94, 2004) and Li and Zhang (J. Opt. Theory Appl. 131:429–452, 2006). We derive sufficient optimality conditions for the bilevel programming problem by using these functions, and we establish various duality results by associating the given problem with two dual problems, namely Wolfe type dual and Mond–Weir type dual.