arXiv subjects

Laurel Travis

Publications and source records attributed to Laurel Travis.

2 recordsLinked to original sources

arXiv2023

Optimizing Representation in Redistricting: Dual Bounds for Partitioning Problems with Non-Convex Objectives

We investigate optimization models for the purpose of computational redistricting. Our focus is on nonconvex objectives for estimating expected Black Representatives and Political Representation. The objectives are a composition of a ratio of variables and a normal distribution's cumulative distribution function (or ``probit curve"). We extend the work of Validi et al.~\cite{validi2022imposing}, which presented a robust implementation of contiguity constraints. By developing mixed integer linear programming models that closely approximate the parent nonlinear model, our approaches yield tight bounds on these optimization problems. We exhibit the effectiveness of these approaches on county-level data.

math.OC↗

arXiv2022

Continuous Equality Knapsack with Probit-Style Objectives

We study continuous, equality knapsack problems with uniform separable, non-convex objective functions that are continuous, antisymmetric about a point, and have concave and convex regions. For example, this model captures a simple allocation problem with the goal of optimizing an expected value where the objective is a sum of cumulative distribution functions of identically distributed normal distributions (i.e., a sum of inverse probit functions). We prove structural results of this model under general assumptions and provide two algorithms for efficient optimization: (1) running in linear time and (2) running in a constant number of operations given preprocessing of the objective function.

math.OC↗