Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 173, Issue 2, Pages 683-703Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-017-1069-4
Keywords
Bilevel programming; Robust optimization; Uncertain linear constraints; Global polynomial optimization; Semidefinite program
Funding
- UNSW Vice-Chancellor's Postdoctoral Research Fellowship [RG134608/SIR50]
- Australian Research Council
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This paper studies a bilevel polynomial program involving box data uncertainties in both its linear constraint set and its lower-level optimization problem. We show that the robust global optimal value of the uncertain bilevel polynomial program is the limit of a sequence of values of Lasserre-type hierarchy of semidefinite linear programming relaxations. This is done by first transforming the uncertain bilevel polynomial program into a single-level non-convex polynomial program using a dual characterization of the solution of the lower-level program and then employing the powerful Putinar's Positivstellensatz of semi-algebraic geometry. We provide a numerical example to show how the robust global optimal value of the uncertain bilevel polynomial program can be calculated by solving a semidefinite programming problem using the MATLAB toolbox YALMIP.
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