Numerically tractable optimistic bilevel problems

Lorenzo Lampariello () and Simone Sagratella ()
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Lorenzo Lampariello: Roma Tre University
Simone Sagratella: Sapienza University of Rome

Computational Optimization and Applications, 2020, vol. 76, issue 2, No 1, 277-303

Abstract: Abstract We consider a class of optimistic bilevel problems. Specifically, we address bilevel problems in which at the lower level the objective function is fully convex and the feasible set does not depend on the upper level variables. We show that this nontrivial class of mathematical programs is sufficiently broad to encompass significant real-world applications and proves to be numerically tractable. From this respect, we establish that the stationary points for a relaxation of the original problem can be obtained addressing a suitable generalized Nash equilibrium problem. The latter game is proven to be convex and with a nonempty solution set. Leveraging this correspondence, we provide a provably convergent, easily implementable scheme to calculate stationary points of the relaxed bilevel program. As witnessed by some numerical experiments on an application in economics, this algorithm turns out to be numerically viable also for big dimensional problems.

Keywords: Bilevel programming; Generalized nash equilibrium problems (GNEP); Leader-follower multi-agent games; Solution methods (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10589-020-00178-y

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