Finding Robust Global Optimal Values of Bilevel Polynomial Programs with Uncertain Linear Constraints

T. D. Chuong () and V. Jeyakumar ()
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T. D. Chuong: University of New South Wales
V. Jeyakumar: University of New South Wales

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 2, No 15, 683-703

Abstract: Abstract 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.

Keywords: Bilevel programming; Robust optimization; Uncertain linear constraints; Global polynomial optimization; Semidefinite program; 49K99; 65K10; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-017-1069-4

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