Continuous Optimization beyond the Black-Box Assumption

Despite their inherent irrationality, people often strive to do things optimally. We want to know the best loan to take out a mortgage or whether buying a climate card will save us money. These problems and many others can be modeled abstractly as minimizing or maximizing some function. These functions can be very complex and depend on millions or billions of variables, so the only way to minimize them is by using iterative algorithms that approach a solution step by step. Mathematical optimization is the field that studies these algorithms. With computer software, some optimization problems can be solved in seconds, while others, such as training certain machine learning models, can take months. Therefore, it is crucial to know the right algorithm for a specific class of functions or to construct even better algorithms for these classes. The goal of this project is precisely this: to further exploit the structure of problems to make algorithms more efficient. Better algorithms will help reduce environmental impact and take us a step closer to making modern AI more explainable.