Robust bilevel optimization for near-optimal lower-level solutions - Systèmes Répartis, Calcul Parallèle et Réseaux
Article Dans Une Revue Journal of Global Optimization Année : 2024

Robust bilevel optimization for near-optimal lower-level solutions

Résumé

Abstract Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution feasibility from limited deviations from the optimal solution at the lower level. General properties and necessary conditions for the existence of solutions are derived for near-optimal robust versions of general bilevel optimization problems. A duality-based solution method is defined when the lower level is convex, leveraging the methodology from the robust and bilevel literature. Numerical results assess the efficiency of exact and heuristic methods and the impact of valid inequalities on the solution time.
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hal-04792534 , version 1 (06-01-2025)

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Mathieu Besançon, Miguel Anjos, Luce Brotcorne. Robust bilevel optimization for near-optimal lower-level solutions. Journal of Global Optimization, 2024, 90 (4), pp.813-842. ⟨10.1007/s10898-024-01422-z⟩. ⟨hal-04792534⟩
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