Deeper Dive
My project focuses on making large optimization problems more computationally manageable by identifying and eliminating hidden redundancies without changing their solutions. Importantly, my method provably enables at least as much compression as methods based on symmetry and permutation invariance. I began this research through MIT PRIMES USA, where I was paired with my mentor based on my interests in applied mathematics, especially optimization. My mentor initially suggested extending an existing reduction technique to a broader class of quadratic problems, but I eventually realized that the same idea could apply more generally to convex optimization. I extended the approach to arbitrary polynomial problems and machine learning, where it can reduce certain training datasets without losing information. By decreasing the time and memory required to solve large problems while preserving their results, I hope this work can make computationally demanding applications of optimization more feasible.
One of the greatest challenges I faced was determining how to evaluate my own work. In my previous research, I could compare my results directly with existing approaches to the same problem. Here, because I was generalizing a mathematical framework into largely unexplored territory, there was no obvious benchmark for determining whether my results were “good enough.” I had to learn to evaluate the work on its own merits.
Because optimization is applied across fields from power systems and communications to medical imaging, I hope my work can help make large-scale optimization more computationally feasible. The next step toward practical use would be incorporating these reduction techniques into widely used solvers, after which researchers and practitioners could apply them to large problems in their respective fields.