Robust bilevel optimization for near-optimal lower-level solutions

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 th...

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Bibliographic Details
Published inJournal of global optimization Vol. 90; no. 4; pp. 813 - 842
Main Authors Besançon, Mathieu, Anjos, Miguel F., Brotcorne, Luce
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2024
Springer Nature B.V
Springer Verlag
Subjects
Approximation
Computer Science
Decision making
Heuristic
Heuristic methods
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Optimization and Control
Random variables
Rationality
Real Functions
Robustness (mathematics)
Bilinear constraints
Bilevel optimization
91A65
Robust optimization
90C46
90C33
Extended formulation
90C34
Decision-dependent uncertainty
Duality
90C26
Bounded rationality
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Summary: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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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-024-01422-z