Benders Subproblem Decomposition for Bilevel Problems with Convex Follower

Geunyeong Byeon, Pascal Van Hentenryck

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications, such as pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel optimization problems in which the upper level problemfeatures some integer variables and the lower level problem enjoys strong duality.We propose a dedicated Benders decomposition method for solving this class of bilevel problems, which decomposes the Benders subproblem into two more tractable, sequentially solvable problems that can be interpreted as the upper and lower level problems.We show that the Benders subproblemdecomposition carries over to an interesting extension of bilevel problems, which connects the upper level solution with the lower level dual solution, and discuss some special cases of bilevel problems that allow sequence-independent subproblem decomposition. Several novel schemes for generating numerically stable cuts, finding a good incumbent solution, and accelerating the search tree are discussed. A computational study demonstrates the computational benefits of the proposed method over a state-of-the-art, bilevel-tailored, branch-and-cut method; a commercial solver; and the standard Bendersmethod on standard test cases and themotivating applications in sequential energymarkets.

Original languageEnglish (US)
Pages (from-to)1749-1767
Number of pages19
JournalINFORMS Journal on Computing
Issue number3
StatePublished - May 2022


  • Benders decomposition
  • bilevel optimization
  • hierarchical decision making
  • mixed-integer bilevel second-order cone programming
  • sequential market clearing

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Computer Science Applications
  • Management Science and Operations Research


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