Title: The Branch-and-Sandwich Algorithm for Mixed-Integer Nonlinear Bilevel Programming Problems
Speaker: Dr. Polyxeni-Margarita Kleniati
Affiliation: Centre for Process Systems Engineering at Imperial College London
Location: Room 144 Huxley
Time: 3:00pm

Abstract. We extend our recently introduced algorithm for general bilevel programming problems, Branch-and-Sandwich (Kleniati and Adjiman, J. Global Optim., 2012), to the class of mixed-integer nonlinear bilevel problems. As in the original algorithm, auxiliary inner lower and upper bounding problems are constructed in order to bound the inner value function and provide constant bound cuts for the outer upper and outer lower bounding problems. The KKT-based relaxations, originally proposed for the inner upper bounding and the outer lower bounding problems, are applicable with respect to the lower-level continuous variables based on appropriate constraint qualifications, but are no longer required. In the extension that we present here, a robust counterpart approach is employed to formulate the inner upper bounding problem and the resulting bound cut may be the only constraint added to the proposed outer lower bounding problem. The branching framework with auxiliary lists of nodes, as developed for the original Branch-and-Sandwich, is also applied to the discrete case. The algorithm is used to solve successfully ten literature problems.

About the speaker. Dr. Kleniati is undertaking her second postdoctoral research position with Prof. Adjiman at the Chemical Engineering department of Imperial College London. She received her PhD in Computing and Optimisation research in 2010 under the supervision of Prof. Rustem at the department of Computing in Imperial College London.
The research of Polyxeni Kleniati is currently focused on the global optimisation of bilevel programming problems with applications to chemical engineering.