Inexact direct-search methods for bilevel optimization problems

Youssef Diouane (), Vyacheslav Kungurtsev (), Francesco Rinaldi () and Damiano Zeffiro ()
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Youssef Diouane: Polytechnique Montréal
Vyacheslav Kungurtsev: Czech Technical University
Francesco Rinaldi: Università di Padova
Damiano Zeffiro: Università di Padova

Computational Optimization and Applications, 2024, vol. 88, issue 2, No 3, 469-490

Abstract: Abstract In this work, we introduce new direct-search schemes for the solution of bilevel optimization (BO) problems. Our methods rely on a fixed accuracy blackbox oracle for the lower-level problem, and deal both with smooth and potentially nonsmooth true objectives. We thus analyze for the first time in the literature direct-search schemes in these settings, giving convergence guarantees to approximate stationary points, as well as complexity bounds in the smooth case. We also propose the first adaptation of mesh adaptive direct-search schemes for BO. Some preliminary numerical results on a standard set of bilevel optimization problems show the effectiveness of our new approaches.

Keywords: Bilevel optimization; Direct search; Convergence analysis (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00567-7

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