Some properties of the bilevel programming problem

By J. Bard. 1991

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Stronger data poisoning attacks break data sanitization defenses (2018, methodology): “…the attacker’s goal as the following optimization problem: This constrained optimization formulation has been used in prior work (e.g., Steinhardt et al., 2017), and despite the approximations, it is still a bilevel problem that is non-convex and intractable to solve exactly (Bard, 1991, 1999).”
Single-leader multi-follower games for the regulation of two-sided Mobility-as-a-Service markets (2021, methodology): “Solution approaches of bilevel programming problem Solving bilevel optimization is a challenging task since even the linear single-leader single-follower problems are NP-hard (Bard 1991). The most common solution approach for linear bilevel programming (LBP) problems is to replace the lower-level pr”
Models for nuclear smuggling interdiction (2007, background): “(1997) and Bard (1998)) each player has an objective function, and these can differ because the players’ motives differ.”
Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints (2003, background): “Problems which fail to have an optimal solution can be found in [30,263].”