CONVERGENT SEMIDEFINITE PROGRAMMING RELAXATIONS FOR GLOBAL BILEVEL POLYNOMIAL OPTIMIZATION PROBLEMS *

V Jeyakumar † (1) , Jean-Bernard Lasserre (2) , G Li (1, 3) , T.S Pham (3)

1 UNSW - University of New South Wales [Sydney]
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
3 DLU - Dalat University [Vietnam]

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 polynomi-als. 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.

Mots clés: bilevel programming; global optimization; polynomial optimization; semidefinite programming hierarchies

Domaines: Optimisation et contrôle [math.OC]

V Jeyakumar †, Jean-Bernard Lasserre, G Li, T.S Pham. CONVERGENT SEMIDEFINITE PROGRAMMING RELAXATIONS FOR GLOBAL BILEVEL POLYNOMIAL OPTIMIZATION PROBLEMS *. SIAM Journal on Optimization, 2016, 26 (1), pp.753--780. ⟨10.1137/15M1017922⟩. ⟨hal-01295159⟩