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Convergent semidefinite programming relaxations for global bilevel polynomial optimization problems

V. Jeyakumar University of New South Wales J.B. Lasserre LAAS-CNRS and Institute of Mathematics, Toulouse Guoyin Li University of New South Wales T.S. Pham University of Dalat

Numerical Analysis and Scientific Computing Optimization and Control mathscidoc:2108.25004

SIAM Journal on Optimization, 26, (1), 753–780, 2016.7
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper-and the lower-level problems are polynomials. We present methods for finding its global minimizers and global minimum using a sequence of semidefinite programming (SDP) relaxations and provide convergence results for the methods. Our scheme for problems with a convex lower-level problem involves solving a transformed equivalent single-level problem by a sequence of SDP relaxations, whereas our approach for general problems involving a nonconvex polynomial lower-level problem solves a sequence of approximation problems via another sequence of SDP relaxations.
bilevel programming, global optimization, polynomial optimization, semidefinite programming hierarchies
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@inproceedings{v.2016convergent,
  title={Convergent semidefinite programming relaxations for global bilevel polynomial optimization problems},
  author={V. Jeyakumar, J.B. Lasserre, Guoyin Li, and T.S. Pham},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210823154522724542863},
  booktitle={SIAM Journal on Optimization},
  volume={26},
  number={1},
  pages={753–780},
  year={2016},
}
V. Jeyakumar, J.B. Lasserre, Guoyin Li, and T.S. Pham. Convergent semidefinite programming relaxations for global bilevel polynomial optimization problems. 2016. Vol. 26. In SIAM Journal on Optimization. pp.753–780. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210823154522724542863.
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