Definition

The general formulation of a bilevel programming problem (BLPP) is

minx∈X,y⁡F(x,y)s.t. G(x,y)≤0miny⁡f(x,y)s.t. g(x,y)≤0 \begin{aligned} \min_{x \in X, y} & F(x,y) \\ \text{s.t. } & G(x,y) \leq 0 \\ \min_y & f(x,y) \\ \text{s.t. } & g(x,y) \leq 0 \end{aligned}

where x∈ℝn1x \in \mathbb{R}^{n_1} (upper-level variables), y∈ℝn2y \in \mathbb{R}^{n_2} (lower-level variables)

See also

References

  1. B. Colson, P. Marcotte, and G. Savard, “An overview of bilevel optimization,” Ann Oper Res, vol. 153, no. 1, pp. 235–256, Sep. 2007, doi: 10.1007/s10479-007-0176-2.
  2. Ye, J. J., & Zhu, D. L. (1995). Optimality conditions for bilevel programming problems. Optimization, 33(1), 9-27. https://doi.org/10.1080/02331939508844060
  3. Wan, Z., & Chen, J. W. (2013). On bilevel variational inequalities. Journal of the Operations Research Society of China, 1(4), 483-510. https://doi.org/10.1007/s40305-013-0036-5
  4. https://en.wikipedia.org/wiki/Bilevel_optimization