Robust bilevel optimization for near-optimal lower-level solutions

Mathieu Besançon (), Miguel F. Anjos () and Luce Brotcorne ()
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Mathieu Besançon: Université Grenoble Alpes, Inria, LIG
Miguel F. Anjos: University of Edinburgh
Luce Brotcorne: Centre Inria de l’Université de Lille, Inria, France and UMR 9189 - CRIStAL, Univ. Lille, CNRS

Journal of Global Optimization, 2024, vol. 90, issue 4, No 1, 813-842

Abstract: 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.

Keywords: Bilevel optimization; Robust optimization; Decision-dependent uncertainty; Bounded rationality; Duality; Bilinear constraints; Extended formulation; 90C33; 90C46; 91A65; 90C26; 90C34 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01422-z

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