Sum of Square

Sum-of-squares (SOS) programming is a powerful optimization technique used to solve challenging problems by representing non-convex constraints as sums of squares of polynomials. Current research focuses on applying SOS to diverse areas, including private data analysis, motion planning verification, and robust control system design, often leveraging its ability to provide certificates of optimality or safety. This approach offers significant advantages in guaranteeing solution quality and safety, particularly in high-dimensional or complex systems, leading to improved algorithms and more reliable results across various scientific and engineering disciplines. The resulting advancements have practical implications in robotics, machine learning, and data privacy.