ORIE Colloquium: Andrea Lodi (Cornell Tech) - Disjunctive Cuts for Mixed-Integer Conic Optimization

Description

This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating conic program for separating disjunctive cuts and investigate the impact of the normalization condition on its resolution. In particular, we show that a careful selection of normalization guarantees its solvability and conic strong duality. Then, we highlight the shortcomings of separating conic-infeasible points in an outer-approximation context and propose conic extensions to the classical lifting and monoidal strengthening procedures. Finally, we assess the computational behavior of various normalization conditions in terms of gap closed, computing time, and cut sparsity. In the process, we show that our approach is competitive with the internal lift-and-project cuts of a state-of-the-art solver.

This is joint work with Mathieu Tanneau and Juan-Pablo Vielma.

Bio:
Andrea Lodi is an Andrew H. and Ann R. Tisch Professor at the Jacobs Technion-Cornell Institute at Cornell Tech and the Technion. He is a member of the Operations Research and Information Engineering field at Cornell University. He received his Ph.D. in system engineering from the University of Bologna in 2000 and he was a Herman Goldstine Fellow at the IBM Mathematical Sciences Department, N.Y. in 2005–2006. He was a full professor of operations research at DEI, the University of Bologna between 2007 and 2015. Since 2015, he has been the Canada Excellence Research Chair in “Data Science for Real-time Decision Making” at Polytechnique Montréal. His main research interests are in mixed-integer linear and nonlinear programming and data science and his work has received several recognitions including the IBM and Google faculty awards. He is the author of more than 100 publications in the top journals of the field of mathematical optimization and data science. He serves as editor for several prestigious journals in the area. He has been the network coordinator and principal investigator of two large EU projects/networks, and, since 2006, consultant of the IBM CPLEX research and development team. Andrea Lodi is the co-principal investigator of the project “Data Serving Canadians: Deep Learning and Optimization for the Knowledge Revolution,” recently funded by the Canadian Federal Government under the Apogée Programme and scientific co-director of IVADO, the Montréal Institute for Data Valorization.