Structured Assignment: Geometric Optimization Algorithms for Large-Scale Matching

This project aimed to develop a mathematical theory and accompanying numerical algorithms for geometrically structured instances of the assignment problem. We considered generalizations of assignment/transportation mathematical programs that included a variety of objective functions, with the commonality that they are parameterized by an underlying distance function along a geometric domain. This additional assumption which arises naturally in applications including 3D shape analysis, logistical operations/planning, and machine learning provides added structure that we leveraged to derive fine-grained understanding of the energy landscape and tractability.