09:45 AM - 10:10 AM
Partially ranked choice models for data-driven large-scale assortment optimization
We propose a new representation for rank-based choice models that generalizes classical representations. The model allows for subsets of products on which the consumer does not have a strict preference. The consumer preferences can be learned via column generation and negative reduced cost columns can be identified efficiently by representing user behaviors in a tree. Empirical results are provided for large artificial and industrial data sets.
10:10 AM - 10:35 AM
Second Order Cone Programming Approach for the flexible target VRP
We present a generalization of the vehicle routing problem which consists of intercepting non-stationary targets with a fleet of vehicles in order to bring them to a common destination. We propose a Mixed Integer Second Order Cone Program for the problem, exploit the problem structure using a Lagrangian decomposition, and propose an exact branch-and-price algorithm.
10:35 AM - 11:00 AM
Cubic Regularization For Symmetric Rank-1 and Nonlinear Conjugate Gradient Methods
Regularization techniques have been used to help existing algorithms solve "difficult" nonlinear optimization problems. Over the last decade, regularization has been proposed to remedy issues with equality constraints and equilibrium constraints, bound Lagrange multipliers, and identify infeasible problems. In this talk, we will focus on the application of cubic regularization in the context of the symmetric rank-one and conjugate gradient methods for nonlinear programming.