Convex Relaxation

Convex relaxation is a technique used to approximate solutions to difficult non-convex optimization problems by reformulating them as convex problems, which are significantly easier to solve. Current research focuses on developing tighter relaxations for various applications, including neural network verification, path planning, and signal processing, often employing algorithms like A*, semidefinite programming (SDP), and block coordinate descent to solve the resulting convex problems. These advancements improve the efficiency and scalability of solving complex problems across diverse fields, leading to more accurate and computationally feasible solutions in areas such as machine learning, robotics, and computer vision. The resulting approximations often provide provable guarantees on solution quality, enhancing the reliability of applications.