EURO 2025 Leeds
Abstract Submission

1239. Exact Solution Method for Nonlinear Bilevel Interdiction Problems: Applications in Investment and Facility Disruption

Invited abstract in session WD-35: Bilevel optimization and augmented Lagrangian methods, stream Continuous and mixed-integer nonlinear programming: theory and algorithms.

Wednesday, 14:30-16:00
Room: Michael Sadler LG15

Authors (first author is the speaker)

1. Suyog Nigudkar
OM,QM,IS, IIM Udaipur
2. Ankur Sinha
Production and Quantitative Methods, Indian Institute of Management Ahmedabad
3. Sachin Jayaswal
Production & Quantitative Methods, Indian Institute of Management Ahmedabad

Abstract

Bilevel optimization is a powerful framework for modeling hierarchical decision-making problems involving multiple players. A significant subset of these problems is the Interdiction Problems, where a leader strategically disrupts the follower’s objective by anticipating their optimal response. While linear interdiction problems have been extensively studied, nonlinear interdiction problems remain underexplored due to their computational complexity, particularly when involving integer variables and nonlinear objectives. This paper introduces an exact solution method for mixed-integer bilevel interdiction problems with nonlinear objectives. The proposed method iteratively refines upper and lower bounds by constructing an inner approximation of the convex hull of the follower’s feasible region and approximating the nonlinear objective using a representative sample of feasible solutions. To demonstrate its effectiveness, we apply the approach to two application problems: (i) a nonlinear knapsack interdiction problem, which models diminishing marginal returns in competitive investment settings, and (ii) a capacitated facility interdiction problem, where interdiction leads to operational disruptions with nonlinear cost effects. Computational experiments demonstrate the efficiency and accuracy of the proposed method, highlighting its potential for addressing complex interdiction scenarios in strategic decision-making applications.

Keywords

Status: accepted

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