Benders Subproblem Decomposition for Bilevel Problems with Convex Follower

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 problems which the upper level problem features some integer variables lower enjoys strong duality. We propose dedicated Benders decomposition method for solving problems, decomposes subproblem into two more tractable, sequentially solvable can be interpreted problems. show carries over to an interesting extension connects solution with dual solution, discuss special cases allow sequence-independent decomposition. Several novel schemes generating numerically stable cuts, finding good incumbent accelerating search tree are discussed. A computational study demonstrates benefits proposed state-of-the-art, bilevel-tailored, branch-and-cut method; commercial solver; standard on test motivating applications sequential energy markets.