Linear Bi-Level Programming Problems -- A Review

An overview of bilevel optimization

“…3.1 below), it is not surprising that most algorithmic research to date has focused on the simplest cases of bilevel programs, that is problems having nice properties such as linear, quadratic or convex objective and/or constraint functions. In particular, the most studied instance of bilevel programming problems has been for a long time the linear BLPP-in which all functions are linear-and therefore this subclass is the subject of several dedicated surveys, such as those by Hsu and Wen (1989), Wen and Hsu (1991) and Ben-Ayed (1993). Over the years, more complex bilevel programs were studied and even those including discrete variables received some attention, as in Vicente et al (1996).…”

Bilevel programming: A survey

“…3.1 below), it is not surprising that most algorithmic research to date has focused on the simplest cases of bilevel programs, that is problems having nice properties such as linear, quadratic or convex objective and/or constraint functions. In particular, the most studied instance of bilevel programming problems has been for a long time the linear BLPP -in which all functions are linear -and therefore this subclass is the subject of several dedicated surveys, such as those by nd Wen(1989)u (s), nd Hsu(1991)n (e) and Ayed(1993)n (e). Over the years, more complex bilevel programs were studied and even those including discrete variables received some attention, as in nte et al (1996) Vicente, Savard, and Júdicec (i).…”

Finding an efficient solution to linear bilevel programming problem: An effective approach

“…They suggest several efficient compromise solutions based on the DMs' preference. However, the optimal solution must be identified before the post-optimality analysis, which is quite time-consuming owing to the complexity of the problem (see [2], [11]). In this paper, a solution procedure is proposed to generate efficient conpromise solutions, without finding the optimal solution in advance.…”