An algorithm for the mixed-integer nonlinear bilevel programming problem

A bi-level programming model and solution algorithm for the location of logistics distribution centers

“…There is rich history of analytic work on the mixed integer bi-level programming problem [17][18][19][20]. However, most of these results deal with the linear objective functions.…”

An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions

“…For example, even if the relaxation solution (61)-(64) turns out to be integral, it cannot be immediately fathomed. The relaxation problem we designed is a more sophisticated parametric HPP (16)- (24), which keeps the integrality requirement constraints (22) and (24) and includes additional constraints (19) and (20). The latter two constraints are designed to provide a tight relaxation of the BMILP.…”

“…Most early studies [8][9][10]27,39] focused on the simpler case of bilevel linear program. Since the 1990s, there has been increased attention on more complex models with nonlinear terms [6,4,21,22] or discrete decision variables [7,19,32,38]. Comprehensive reviews of existing bilevel optimization algorithms and applications can be found in [15,37].…”

Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints

“…Such algorithms are the following: branch-and-bound algorithms for exact and approximate solutions [130,300,433]. Algorithms being based on parametric linear discrete optimization can be found in the papers [120,195,196], and a cutting plane algorithm in [112].…”