Operations Research 2025
Abstract Submission

2207. Column-and-Constraint Generation for Robust Bilevel Optimization with Wait-and-See Follower

Invited abstract in session WC-4: Bilevel and Mixed-Integer Nonlinear Programming, stream Continuous and Global Optimization.

Wednesday, 13:30-15:00
Room: H6

Authors (first author is the speaker)

1. Johannes Thürauf
Discrete Optimization, University of Technology Nuremberg
2. Henri Lefebvre
Department of Mathematics, Universität Trier

Abstract

Bilevel optimization is a mathematical framework that allows modeling of hierarchical decision processes. Typically, it is assumed that all input parameters for both the leader and the follower are known when the leader makes a decision. However, in many real-world applications, the leader has to decide without fully anticipating the follower's response due to uncertainties in the follower's problem. In this talk, we address robust bilevel optimization problems in which the follower adopts a so-called wait-and-see approach. In this setting, the leader decides without knowledge of the specific realization of the uncertainty. Then, the uncertainty realizes in a worst-case manner, and afterward the follower makes their own decisions. For this challenging problem class, we discuss mathematical properties and present a corresponding solution approach based on column-and-constraint generation. The convergence of the proposed algorithm is discussed along with its practical implementation including numerical results.

Keywords

Status: accepted

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