Tuesday 24 September

Polynomial Optimization Techniques for Machine Learning and Supply Chain Management

Georgina Hall, INSEAD

Abstract:

In this talk, we consider two optimization problems, one in machine learning and one in supply chain management, that can be formulated as polynomial optimization problems (POPs). The first one involves fitting a polynomial to data, with the twist that this polynomial has constraints on its shape (e.g., it is required to be convex or increasing in one variable). The second one involves choosing the smallest set of firms in a supply chain network to whom to give free traceability technology in the hope of disseminating this technology across the whole network. We show that both problems are NP-hard to solve and use techniques from POPs to provide workarounds to the hardness. To address the first problem, we provide a hierarchy of semidefinite programs and show that polynomial functions that are optimal to any fixed level of our hierarchy form a consistent estimator of the underlying shape-constrained function.  For the second problem, we provide a fixed-parameter tractable algorithm in the treewidth of the supply chain network. We show that this treewidth is low in real-world supply chains and leverage the algorithm to conduct large-scale numerical experiments that provide insights into how the supply chain network structure influences diffusion.

This talk combines two papers:

– Shape-Constrained Regression Using Sum of Squares Polynomials, M. Curmei and G. Hall, Operations Research, 2023. https://doi.org/10.1287/opre.2021.0383

– Traceability Technology Adoption in Supply Chain Networks, P. Blaettchen, A. Calmon, and G. Hall, Management Science, 2024. https://doi.org/10.1287/mnsc.2022.01759

Registration, please contact robin@em-lyon.com

Salle B2-122, Lyon campus