Polynomial Optimization

Polynomial optimization focuses on finding the minimum or maximum of a polynomial function, often subject to polynomial constraints—a challenging non-convex problem with broad applications. Current research emphasizes developing efficient and certifiably correct algorithms, such as those based on sum-of-squares (SOS) relaxations, semidefinite programming (SDP), and Chebyshev polynomial approximations, to tackle these problems. These advancements are improving the accuracy and speed of solutions in diverse fields, including robotics, quantum system identification, and machine learning, by enabling more robust and reliable optimization within complex systems. The development of sparse and scalable algorithms is a key focus to address the computational challenges associated with large-scale problems.