(147aa) Nonconvex Optimization Problems Involving the Euclidean Distance

Nonconvex optimization problems involving the Euclidean distance arise in diverse settings such as facility location, molecular energy minimization, and object packing. These problems present a challenge for global optimization algorithms based on spatial branch-and-bound since they exhibit a high degree of symmetry, and factorable relaxations of reverse convex constraints and compositions of functions with norms are generally weak. Global minima have been found for small instances, but many problems remain open.

In this work, we introduce novel geometry-informed techniques for constructing convex relaxations of nonconvex problems involving the Euclidean distance. We implement our methods in the global optimization solver BARON and demonstrate their impact using open problems from the literature as a benchmark.

Research Interests: I am passionate about developing tools for challenging computational problems in science and engineering. My expertise is in mathematical optimization, where I have experience in modeling, algorithm development, and computational implementation of results. I am interested in opportunities to contribute to state-of-the-art computing technology while further developing my skills, particularly in applied math, software development, and operations research.