Near-optimal robust bilevel optimization
Document type :
Pré-publication ou Document de travail
Title :
Near-optimal robust bilevel optimization
Author(s) :
Besançon, Mathieu [Auteur]
Inria Lille - Nord Europe
Centrale Lille
École Polytechnique de Montréal [EPM]
Integrated Optimization with Complex Structure [INOCS]
Anjos, Miguel [Auteur]
School of Mathematics - University of Edinburgh
École Polytechnique de Montréal [EPM]
Brotcorne, Luce [Auteur]
Inria Lille - Nord Europe
Integrated Optimization with Complex Structure [INOCS]
Inria Lille - Nord Europe
Centrale Lille
École Polytechnique de Montréal [EPM]
Integrated Optimization with Complex Structure [INOCS]
Anjos, Miguel [Auteur]
School of Mathematics - University of Edinburgh
École Polytechnique de Montréal [EPM]
Brotcorne, Luce [Auteur]
Inria Lille - Nord Europe
Integrated Optimization with Complex Structure [INOCS]
English keyword(s) :
bilinear constraints
robust optimization
game theory
bilevel optimization
bounded rationality
duality
robust optimization
game theory
bilevel optimization
bounded rationality
duality
HAL domain(s) :
Mathématiques [math]/Optimisation et contrôle [math.OC]
English abstract : [en]
Bilevel optimization problems embed the optimality conditions of a sub-problem into the constraints of another optimization problem. We introduce the concept of near-optimality robustness for bilevel problems, protecting ...
Show more >Bilevel optimization problems embed the optimality conditions of a sub-problem into the constraints of another optimization problem. We introduce the concept of near-optimality robustness for bilevel problems, protecting the upper-level solution feasibility from limited deviations at the lower level. General properties and necessary conditions for the existence of solutions are derived for near-optimal robust versions of generic bilevel 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 the proposed algorithm and the impact of valid inequalities on the solution time.Show less >
Show more >Bilevel optimization problems embed the optimality conditions of a sub-problem into the constraints of another optimization problem. We introduce the concept of near-optimality robustness for bilevel problems, protecting the upper-level solution feasibility from limited deviations at the lower level. General properties and necessary conditions for the existence of solutions are derived for near-optimal robust versions of generic bilevel 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 the proposed algorithm and the impact of valid inequalities on the solution time.Show less >
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Anglais
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