Seminar by Mustafa Rasim Kılınç

The focus of this work is a computationally effective method for generating disjunctive cuts for convex MINLPs. The method relies on solving a sequence of cut- generating linear programs (CGLP). If the constraint functions have a special separability structure, then the polyhedral outerapproximation of the feasible region can be significantly improved by introducing auxiliary variables that separately approximate the elements of the constraint functions. These improved approximations can have significant positive benefits for linearization-based algorithms as well as the performance of the disjunctive cut generation method. The introduction of auxiliary variables can also improve the strength of the generated cuts. For instance, we have recently shown that, while the conic MIR proposed by Atamturk and Narayanan only uses an LP approximation to generate cuts for conic integer programming, the use of an extended formulation can allow the conic MIR to outperform cuts that use all the nonlinear relaxation. Our computational experiments compare the strength of this and other extended formulations for cutting plane generation and explore the strength of extensions of the conic MIR that use additional nonlinear information. This talk is based on joint work with S. Moderasi, J. Linderoth, J. Luedtke and J.P. Vielma.