Session: Global Optimization Theory and Algorithms
Chair: Sergiy Butenko
Cluster: Global Optimization
Talk 1: Solving bilevel polynomial optimization by disjunctive decomposition
Speaker: Suhan Zhong
Abstract: We consider bilevel polynomial optimization problems whose lower level constraints are linear on lower level variables. We show that such a bilevel program can be reformulated as a disjunctive program using partial Lagrange multiplier expressions. Each branch problem of this disjunctive program can be efficiently solved by polynomial optimization techniques. We give necessary and sufficient conditions for solutions of branch problems to be global optimizer of original bilevel optimization, and sufficient conditions for the local optimality.
Talk 2: Adaptive Bilevel Knapsack Interdiciton
Speaker: Jourdain Lamperski
Abstract: We consider adaptive bilevel knapsack interdiction. A leader aims to interdict items that a follower aims to fill their knapsack with. The leader does not have full information, as captured by a finite number of possible realizations of the follower. The leader can adapt to uncertainty by executing one of a budgeted number of precomputed interdiction policies. We propose exact and approximate solution methods. In particular, we present theoretical performance guarantees for the approximate solution methods and evalutate their empirical performance against the exact methods through computational experiments.
Talk 3: Continuous Approaches to Cluster-Detection Problems in Networks
Speaker: Sergiy Butenko
Abstract: We discuss continuous formulations for several important cluster-detection problems in networks. More specifically, the problems of interested are formulated as quadratic, cubic, or higher-degree polynomial optimization problems subject to linear constraints. The proposed formulations are used to develop analytical bounds as well as effective algorithms for some of the problems. Moreover, a novel hierarchy of nonconvex continuous reformulations of optimization problems on networks is discussed.
