Is bilevel programming a special case of a mathematical program with complementarity constraints?

Topological Aspects of Nonsmooth Optimization

“…Then, it is well-known that y ∈ Argmin L(x) if and only if there exist Lagrange multipliers µ j ∈ R, j ∈ J such that: Here, complementarity constraints are µ j ≥ 0, h j ≥ 0, µ j h j (x, y) = 0. The links between U and U -KKT were elaborated in [18]. It turns out that global solutions of U and U -KKT coincide.…”

A Smoothing Method for Solving Bilevel Multiobjective Programming Problems

“…ðA 2 Þ At each x 2 P x and y 2 " S, the lower level problem ðP x Þ is a convex parameter multiobjective program, and the partial gradient r y g i ðx; yÞ; i 2 Iðx; yÞ is linearly independent. Remark 2.3 It is noted that the assumption ðA 2 Þ plays a key role in the method of replacing the lower level problem with its KKT optimality conditions [9]. Based on assumption ðA 2 Þ, we can adopt the method of replacing the lower level problem with its KKT optimality conditions, and transform the bilevel programming into the corresponding single-level programming problem.…”

Variational Analysis of Marginal Functions with Applications to Bilevel Programming

“…The major goal of this paper is to derive new necessary optimality conditions for a class of bilevel programs the importance of which has been well recognized in optimization theory and applications; see, e.g., the book by Dempe [6], the more recent publications [7,8,10,26,28], and the bibliographies therein among other references that mostly concern bilevel programming in finite dimensions. Here we consider bilevel programs in infinite dimensions while all the results obtained are new in the standard framework of finite-dimensional spaces.…”